Improving Rock Classification with 1D Discrete Wavelet Transform Based on Laboratory Reflectance Spectra and Gaofen-5 Hyperspectral Data

Abstract

The high intra-class variability of rock spectra is an important factor affecting classification accuracy. The discrete wavelet transform (DWT) can capture abrupt changes in the signal and obtain subtle differences between the spectra of different rocks. Taking laboratory spectra and hyperspectral data as examples, high-frequency features after DWT were used to improve the discrimination accuracy of rocks. Various decomposition levels, mother wavelet functions, and reconstruction methods were used to compare the accuracy. The intra-class variability was measured using the intra-class Spectral Angle Mapper (SAM). Our results show that the high-frequency features could improve the discrimination accuracy of laboratory spectra by 13.4% (from 46.5% to 59.9%), compared to the original spectral features. The accuracy of image spectra in two study areas increased by 8.6% (from 68.3% to 76.9%) and 7.2% (from 81.3% to 88.5%), respectively. Haar wavelets highlighted the spectral differences between different rocks. After DWT, intra-class SAM reduced and intra-class variability of rocks decreased. The Pearson correlation coefficient indicated a negative correlation between intra-class variability and overall accuracy. It suggested that improving classification accuracy by reducing intra-class variability was feasible. Though the result of lithological mapping still leaves room for improvement, this study provides a new approach to reduce intra-class variability, whether using laboratory spectra or hyperspectral data.

1. Introduction

Remote sensing is an important tool for obtaining lithology maps while saving costs [1,2]. Although some geologists argue that remote sensing may not provide accurate results for creating lithology maps, the combination of field surveys and remote sensing can significantly improve the efficiency of lithological mapping [3].

Airborne imaging spectrometers were used for geological mapping in earlier studies [4]. Greenbaum et al. [5] used 11-band airborne multispectral scanner data to discriminate lithology in central Snowdonia. They found that the Optimal Index Factor (OIF) and principal component images were helpful for sediment identification. With the development of satellite remote sensing, large-scale and high-frequency observations became possible [6]. The Landsat series, Sentinel-2, and other multispectral sensors are widely used for lithology classification [7,8]. Pal et al. [9] proposed an image fusion method and applied the method to Sentinel-2, Landsat 8, and ASTER data to improve rock discrimination accuracy. Rowan et al. [10] performed ASTER ratio imaging, matched-filtering, and spectral-angle mapping for lithological classification. Spectral reflectance and emissivity data were utilized to distinguish between four mafic-ultramafic categories, three categories of alluvial-colluvial deposits, and a quartzite unit. In addition to multispectral data, hyperspectral data like Earth Observing-1 (EO-1) Hyperion and GaoFen-5 (GF-5) Advanced Hyperspectral Imager (AHSI) provide more detailed spectral information for geological bodies [11]. Guo et al. [12] utilized the semi-supervised self-learning (SSL) method to investigate the capability of Hyperion data in lithological classification with limited samples. Zhang et al. [13] mapped areas of acicularite and sericite using GF-5 AHSI data and proposed indicators of uranium mineralization. Shebl et al. [14] tested the ability of the PRecursore IperSpettrale della Missione Applicativa hyperspectral data for lithological mapping, and the Support Vector Machine algorithm achieved the highest accuracy. The abundant spectral information makes mineral mapping possible. The extraction of mineral content helps improve the discrimination accuracy of altered rocks [15]. For example, minerals such as hematite, goethite, and jarosite show significant absorption in the visible-to-near-infrared (VNIR) range of 400–1100 nm. Chlorite and clay minerals exhibit absorption peaks in the shortwave infrared (SWIR) range [16]. A combination of hyperspectral and multi-temporal multispectral data has been proven to improve mineral identification accuracy [17]. Liu et al. [18] used Landsat TM data from the same season in four different years to eliminate the random interference of alteration minerals and also used Hyperion data to identify alteration minerals around granites.

Geological mapping using image spectra was often combined with laboratory spectra [19,20]. Using a handheld spectrometer is the easiest way to obtain spectra for rock samples. The spectra obtained with spectrometers are more suitable for studying the physicochemical properties of rocks and avoiding pixel mixing [21]. Wang et al. [22] collected the reflectance spectra of rocks and minerals in Xinjiang, China, using a spectrometer and established a spectral library, which is of great significance for accelerating regional geological research.

Various spectral transformation algorithms and classification algorithms were used to improve the accuracy of rock or mineral extraction from hyperspectral data. Kumar et al. [23] used different spectral enhancement techniques (Principal Component Analysis and Independent Component Analysis) and machine learning algorithms to improve the accuracy of hyperspectral lithology identification, and the results showed that the optimal band based on Joint Mutual Information Maximization had the best classification results. Tan et al. [24] utilized an efficient clustering algorithm based on affinity propagation to select fewer bands with higher lithological discrimination capability. Unlike vegetation and crops, the same kind of rock may have diversified spectral curves (especially different spectral intensities) due to different mineral composition, mineral content, weathering, etc. [25]. High intra-class variability may lead to spectral confusion and poor classification accuracy [26]. Previous studies used the first derivative of spectra combined with the original spectra for classification [27].

Wavelet transform is a powerful method for extracting features of signals, which can obtain features in both time and frequency domains [28]. The number of features remains the same after decomposition and reconstruction. High-frequency components give details in the signal and can highlight abrupt changes in the spectra [29]. Although rock spectra have high intra-class variability, spectral curves of the same type of rock may have similar absorption characteristics [30,31]. Wavelet transform has advantages in extracting subtle features [32,33]. Chen et al. [34] proposed an adaptive wavelet filter for image denoising, which can effectively reduce the variable band noise of different targets. In the area of geological mapping with spectroscopy and hyperspectral sensors, Lorenz et al. [35] found that wavelet-based sparse reduced-rank regression classified geological bodies more accurately than Principal Component Analysis (PCA) and Minimum Noise Fraction (MNF). Feng et al. [36] used Continuous Wavelet Analysis (CWA) to improve the radiometric quality of images by minimizing random noise and enhancing spectral features, with good results in mapping ultramafic rock units. Mitchley et al. [37] improved the accuracy of mineral content estimation via wavelet denoising. In previous studies, low-frequency features were extracted for signal smoothing and filtering [38], while high-frequency features were often considered as noise. Using high-frequency features to improve rock classification accuracy was rarely mentioned.

A random forest classifier is an efficient machine learning algorithm [39]. Random forests were often used for image classification in remote sensing, whether for multispectral data [40], hyperspectral data [41], or synthetic aperture radar data [42]. A random forest classifier can handle datasets with a large number of features and samples and avoid overfitting. Efficient and stable classifiers are necessary for studying the improvement of classification accuracy with wavelet transform. During the evaluation of different decomposition and reconstruction approaches, a random forest classifier was used to classify rocks or rock units. Spectral Angle Mapper (SAM) was widely used in geological mapping, describing the similarity between the target spectrum and a reference spectrum [43]. SAM has also been used to assess intra-class variability [27].

This paper aims to test the ability of wavelet-transformed high-frequency features to improve hyperspectral lithology discrimination. The specific contents include (1) wavelet decomposition of hand-specimen spectra and image spectra and reconstruction of high-frequency coefficients; (2) detecting the intra-class variability of spectral curves before and after wavelet transform; (3) selecting the best mother wavelet function, decomposition level, and reconstruction method for lithology classification; and (4) geological mapping in areas with rock outcrops and less vegetation.

2. Study Area and Data

2.1. Field Rock Samples for Laboratory Spectral Measurements

The rock samples were collected from Huludao City, Liaoning Province, China, in 2013 and 2015. This area is located in the North China Craton, which is an important constituent unit of the continental lithosphere and has experienced multiple phases of regional tectonic evolution. The study area is rich in vegetation types dominated by pine, cypress, and pagoda trees. Rocks from the Mesozoic and Mesoproterozoic eras were collected. Weathered surfaces were removed as much as possible during sample collection. The samples were classified into six types based on their mineralogical composition, including 46 samples of dolostone, 55 samples of andesite, 82 samples of tuff, 109 samples of limestone, 66 samples of sandstone, and 121 samples of granite (

Table 1. Names and photos of rock samples collected in the field.

Name	Photo	Name	Photo
dolostone		andesite
tuff		limestone
sandstone		granite

).

Dolostone is composed primarily of dolomite, often mixed with quartz, feldspar, calcite, and clay minerals. Andesite is a kind of neutral ejecta with small amounts of plagioclase feldspar, hornblende, pyroxene, and the porphyry of biotite. Tuff is the most common type of volcaniclastic rock and generally contains a variety of clastic materials. Limestone is a class of carbonate rocks with calcite as the main component. Sandstone is mainly composed of various sand particles cemented together, with a particle diameter of 0.05–2 mm. The cement in the sandstone is dominated by quartz, feldspar, calcite, and clay minerals. Granite is an important constituent of the continental crust and is widely distributed. The major minerals in granite are quartz, potassium feldspar, and plagioclase, while minor minerals are smectite and hornblende.

2.2. Study Area for Lithological Mapping

Study areas A and B for hyperspectral image classification were selected in the eastern Tianshan region of Xinjiang, China. There are many rock outcrops and little vegetation in the areas, making them suitable for rock unit classification using remote sensing techniques [44]. The reason for choosing two study areas with different elevations and surface relief was to test whether the ability of the discrete wavelet transform to improve lithological mapping is affected by surface morphology. Compared to study area B, the elevation in study area A is higher, and study area A has a high degree of topographic relief. A large area of moyite is exposed in the southwest, and the rock types in study area A are mainly granite, granodiorite, and volcanic rock. The elevation and topographic relief are lower in study area B. Alluvium and fluvial deposits, granite, volcanic rocks, and continental clastic rocks are mainly composed of the northern part. Samples from field surveys are marked with red circles in Figure 1. To verify the accuracy of the geological map, we conducted field validation in some areas, which helped in the selection of image samples in the next step. For field samples, we set more sample points in complex rock units or rock groups and fewer sample points in rocks with obvious remote sensing interpretation signs, such as granite. Rock units Qp²W and Qp³X in the northern part of study area B have complex compositions (sandstones, loess, alluvial deposits, etc.), and we made intensive field observations. The geological maps of the two study areas are shown in Figure 2.

2.3. Gaofen-5

GF-5 is one of the satellites in China’s High-Resolution Earth Observation System. GF-5 carries six types of payloads, and the payload used in this study is AHSI (

Table 2. The parameters of GF-5 AHSI.

Parameters	GF-5 AHSI
Orbit altitude	705 km
Swath width	60 km
Spatial resolution	30 m
Spectral resolution	VNIR: 5 nm; SWIR: 10 nm
Number of bands	VNIR: 150; SWIR: 180
Spectral range	0.39–2.51 μm
SWIR Signal-to-Noise Ratio (SNR)	~500
Dispersive systems	Grating

). There are 150 bands in VNIR and 180 bands in SWIR. The spatial resolution of the data is 30 m. The data acquired on 29 October 2019 (study area A) and 31 May 2019 (study area B) were selected. The full width half max (FWHM) was shown in Figure 3.

3. Methods

Figure 4 shows the workflow of this study. The method primarily consists of four parts: (1) spectral measurement of rocks and preprocessing of GF-5 AHSI data; (2) discrete wavelet transform of laboratory spectra and image spectra; (3) lithology classification and intra-class variability measurement; and (4) accuracy evaluation.

3.1. Laboratory Spectral Processing

3.1.1. Spectral Measurement

The spectra of rocks were measured in the laboratory using the Analytical Spectral Device (ASD) FieldSpec 3. The spectrum ranges from 350 to 2500 nm. The sampling interval is 1.4 nm for 350–1000 nm and 2 nm for 1000–2500 nm. The final spectra were interpolated and output at 1 nm intervals. The distance between the rock sample and the probe was approximately 20 cm during the measurement. This distance is comparable to the size of the rocks. Calibration was performed every ten minutes using a whiteboard. During the spectral measurement, tests were taken on fresh surfaces of rocks, and the average of ten tests was calculated. This helped to avoid errors caused by uneven rock surfaces.

3.1.2. One-Dimensional Discrete Wavelet Transform

Discrete wavelet transform (DWT) is a discretized sampling of the scale and translation parameters for the continuous wavelet transform. DWT can extract the detail and approximation features of signals (Figure 5). One-dimensional (1D) discrete wavelet decomposition and reconstruction were performed on all spectra. At each decomposition level, only the low-frequency coefficients of the signal were decomposed. Daubechies (db) series wavelets have good time and frequency localization properties [46]. The mother wavelet functions (MF) used in this study include db1 (haar), db2, db4, db8, and db10. For dbN wavelets, N is the vanishing moment, and the support length is 2N-1. When the vanishing moment is high, the wavelet coefficients of the high-frequency sub-bands are small, and the computational complexity of the wavelet transform is high. The wavelet function and the scaling function are shown in Figure 6.

Table 3. Four decomposition–reconstruction methods and abbreviations were used in the study.

Decomposition–Reconstruction Method	Abbreviation (Using Haar Wavelets as an Example)
Reconstruct the high-frequency coefficients of the second and third levels after the three-level decomposition	haar_3_23
Reconstruct all three high-frequency coefficients after three-level decomposition	haar_3_123
Reconstruct the high-frequency coefficients of the second, third, and fourth levels after four-level decomposition	haar_4_234
Reconstruct all four high-frequency coefficients after four-level decomposition	haar_4_1234

shows four different decomposition–reconstruction methods, in which each MF performs all decomposition–reconstruction methods. The naming abbreviation rule is MF_decomposition level_high-frequency coefficient level used during reconstruction. Finally, twenty sets of high-frequency features were obtained. DWT was implemented in the wavelet toolbox of Matlab R2023a, which was developed by MathWorks Inc. (Natick, MA, USA) [47,48].

3.1.3. Random Forest Classification

To retain as much spectral information as possible, we did not resample the spectral curves. The basic unit of the random forest (RF) algorithm is the decision tree. Samples are fed into each tree for classification. The classification results of several weak classifiers are voted on and selected to form a strong classifier. RF has advantages in processing high-dimensional data and can provide feature importance rankings during classification [49]. RF was implemented in R 4.2.3 [50], with mtry and ntree as two important parameters. Ntree is the number of trees to grow. Mtry controls how many features are available to be considered for each new split. Mtry was often set to the square root of the number of features, and in the classification of laboratory spectra, it was set to 46. Ntree was set to 1000, which was commonly considered a stable value.

To avoid overfitting and underfitting, five-fold cross-validation was used in the classification [51]. Each type of rock sample was divided into five equal parts, with four parts used for training the model and one part used for model validation. The overall accuracy (OA), Kappa coefficient, and F1-Score after cross-validation were used to assess the classification accuracy.

3.2. Image Spectral Processing

3.2.1. GF-5 AHSI Data Preprocessing

GF-5 AHSI data need to be preprocessed before extracting the image spectra, and the preprocessing was implemented in Pixel Information Expert-Hyp (PIE-Hyp) of PIESAT Information Technology Co., Ltd., Beijing, China (Figure 7). First, the VNIR and SWIR bands were stacked. We used the Stripe Removal module of the software to reduce the stripes in the image. We selected the column with better imaging quality, which was considered to be free of stripes, calculated its mean and variance, and used this column as a reference to adjust the pixel values of other columns. The oxygen absorption peak at 762 nm was used to detect the smile effect [52]. The need for smile correction was determined by observing whether the difference images of the VNIR Band 87 and VNIR Band 89 had a significant brightness gradient. The GF-5 data used in this study were less affected by the smile effect and did not require smile correction. Next, digital numbers were calibrated to the top of the atmosphere reflectance, and the 6S radiative transfer model was used to generate surface reflectance products. Orthorectification was used to remove the effects of terrain. The resampling method was set to the nearest neighbor method, and the output data had a spatial resolution of 30 m. Finally, the bands affected by atmospheric water absorption and those with significant noise were excluded.

Table 4. Bands removed in GF-5 AHSI data preprocessing.

Wavelength Range	Band Number	Wavelength
VNIR	VNIR 1–4	390–403 nm
SWIR	SWIR 1–4	1004–1030 nm
	SWIR 43–50	1359–1418 nm
	SWIR 96–112	1805–1940 nm

shows the excluded bands.

The samples were selected with reference to the geological map. We randomly selected 300 pixels for each type of rock unit as samples. The pixel spectra of the rock units after preprocessing are shown in Figure 8. Pξγ and (E₃-N₁)t have the highest spectral intensity. Compared to study area A, the distribution of image spectra of rock units in study area B is more dispersed. In the range of 1000–2400 nm, the spectral intensities of rock units are significantly different in study area B. For study area A, C₁x, C₁gd, P₁aer, Pγδ, and Pγδπ have overlapping curves that are difficult to distinguish.

3.2.2. One-Dimensional Discrete Wavelet Transform

For a 297-dimensional hyperspectral image, the spectrum of each pixel can be extracted. The extracted spectral curves have 297 bands. For each pixel in the image, a 1D DWT was performed using the same decomposition–reconstruction methods as shown in Table 3.

3.2.3. Random Forest Classification and Accuracy Assessment

The algorithm for geological mapping was the RF algorithm. The number of ntrees was set to 1000, and mtry was set to 17. Similar to laboratory spectral classification, five-fold cross-validation was used for image spectral classification. OA, Kappa coefficient, and F1-Score were also used to evaluate the accuracy. Based on these indicators, the best MF, decomposition level, and reconstruction method were selected. Finally, all pixels in the image were classified. The results using the high-frequency features were compared to those classified using the original features.

3.3. Evaluation of Intra-Class Variability

SAM was used to evaluate spectral variability with the following equation [53]:

$$\alpha ={\cos }^{-1}\left(\frac{x_1^T{x}_2}{\sqrt{x_2^T{x}_2}\sqrt{x_1^T{x}_1}}\right)$$

(1)

where x₁ or x₂ denotes the laboratory spectrum or image spectrum.

The principle of SAM is to consider each spectrum as a high-dimensional vector and measure the similarity of spectra by calculating the angle between two vectors. For the same type of rock, the intra-class SAM between each rock sample and all other rock samples were calculated. The mean and standard deviation of SAM were used to describe intra-class variability. If the mean value of SAM is small, it indicates that the intra-class variability of this rock type is low. The curves after DWT need to be normalized before calculating the intra-class SAM. The following normalization equation was used for the curves after DWT.

$$d^{\prime }=\frac{d-d_{\min }}{d_{\max }-d_{\min }}$$

(2)

where d denotes laboratory spectrum or image spectrum after DWT. When d denotes the laboratory spectrum, d_max and d_min represent the maximum and minimum values of all laboratory spectra after DWT. When d denotes the image spectrum, d_max and d_min represent the maximum and minimum values of all image spectra after DWT.

The Pearson correlation coefficient was used to describe the relationship between classification accuracy and intra-class variability [54].

4. Results

4.1. Laboratory Spectral Classification

4.1.1. DWT of Spectral Curves

Figure 9 shows the original spectral curves and reconstructed curves of various rocks. The reflectance ranges from 0.15 to 0.4. Granite has high reflectance in the 500–1500 nm range. The reflectance curve has a high positive slope in the 0.4–0.6 μm range and exhibits an iron absorption peak near 1 μm and water absorption peaks at 1.4 μm and 1.9 μm. The absorption feature near 2.2 μm may be due to clay alteration. Andesite has low overall reflectance and water absorption peaks at 1.4 μm and 1.9 μm. Limestone exhibits an absorption peak at 2.3 μm, which is different from other rocks [55]. In addition to water absorption features, the average reflectance spectrum of limestone has a carbonate vibration absorption peak at 2.3 μm. Sandstone exhibits absorption peaks at 1.4 μm, 1.9 μm, and 2.2 μm. In the reconstructed curves, intervals with flat spectral curves (e.g., 1500–1800 nm) are reconstructed close to zero. The position where the curve undergoes a sudden change forms a peak in the reconstructed curve.

Figure 10a shows the spectral curves and the average curve of all granite samples. It shows high intra-class variability in rocks, which may lead to poor classification accuracy. Figure 10b shows the high-frequency curve after DWT (haar_4_1234). Compared with Figure 10a, the intra-class variability decreases, and the curve distribution is more concentrated.

4.1.2. Intra-Class Variability

We calculated the mean (Figure 11) and standard deviation (Figure 12) of intra-class SAM using different decomposition–reconstruction methods. If the SAM angle is greater than 0.1, then generally the spectra are considered different. The mean is greater than 0.2, which suggests that there is significant variability in the class or that there are multiple classes. The mean value of intra-class SAM for all rocks is greater than 0.1. After wavelet decomposition and reconstruction, regardless of the choice of MF, the mean and standard deviation of SAM decreased. This indicates that after DWT, the curve distribution of the same type of rock becomes more concentrated.

It can be observed that for limestone, original spectra have the highest mean of SAM, and the use of three different wavelet decomposition–reconstruction methods (db4_4_1234, db8_4_1234, and db10_4_1234) all show the lowest mean of intra-class SAM values. This may indicate that the spectral curves of the limestone samples have different intensities but similar absorption peaks. The high-frequency features of granite samples show the lowest standard deviation of intra-class SAM values compared to the original spectra, regardless of which MF was used. This observation might be related to the spectral distribution of granite samples being more concentrated after DWT.

4.1.3. Classification Results

OA using original features was 0.465 (ranking 17), with a Kappa coefficient of 0.335. Haar_4_1234 has the highest OA of 0.599 (

Table 5. OA and Kappa coefficients of laboratory spectra.

Features	OA	Kappa Coefficients
haar_4_1234	0.599	0.502
haar_4_234	0.595	0.496
db2_4_234	0.593	0.493
haar_3_23	0.580	0.476
haar_3_123	0.574	0.467
db2_4_1234	0.572	0.465
db4_4_1234	0.556	0.441
db4_4_234	0.556	0.443
db2_3_23	0.551	0.435
db10_4_234	0.535	0.413
db2_3_123	0.530	0.405
db10_4_1234	0.526	0.403
db8_4_234	0.514	0.384
db8_4_1234	0.511	0.380
db4_3_23	0.489	0.346
db4_3_123	0.474	0.324
original spectrum	0.465	0.335
db10_3_23	0.443	0.277
db10_3_123	0.432	0.262
db8_3_123	0.430	0.260
db8_3_23	0.428	0.257

). Means and standard deviations for 5-fold cross-validation of laboratory spectral classification are shown in Figure A1 in Appendix A. Features decomposed and reconstructed using haar and db2 wavelets were ranked high. The OA of four-level decomposition was better than the three-level decomposition. The MF with smaller vanishing moments performed better than those with larger vanishing moments.

We computed the highest F1-Score for each type of rock (

Table 6. The highest value of F1-Score among the rock samples on laboratory spectra using high-frequency features.

Rock Types	Highest F1-Score	Features (Highest F1-Score)	F1-Score of Haar_4_1234	Haar_4_1234 Ranking	Original F1-Score	Original F1-Score Ranking
Dolostone	0.689	db2_4_234	0.655	7	0.464	18
Andesite	0.418	db2_4_234	0.383	2	0.271	9
Tuff	0.519	db2_3_123	0.462	4	0.398	18
Limestone	0.665	Haar_4_1234	0.665	1	0.457	21
Sandstone	0.465	Haar_4_234	0.456	2	0.270	8
Granite	0.743	Haar_4_234	0.740	2	0.643	16

). The highest F1-Score was from granite at 0.743. The lowest F1-Score was from andesite, at 0.418. The F1-Score of limestone was improved by 0.208 after DWT, which was the highest for all rocks. The best accuracy for all rocks came from the high-frequency features produced by the db2 wavelet and the haar wavelet. F1-Scores using the original features ranked low. Limestone spectra transformed by DWT obtained better accuracy than the original spectrum, no matter what kind of decomposition and reconstruction method was used.

We tested the overall accuracy of haar_4_1234 using different values of ntree and mtry, which helped to find suitable parameters for laboratory spectra (Figure 13). When the range of the ntree was 300–900 and the range of the mtry was 35–50, the classification accuracy was relatively good. High ntree values increased the training time and might also lead to low classification accuracy. In our experiments, the model achieved the highest overall accuracy of 0.602 when the ntree was 500 and the mtry was 50 or when the ntree was 300 and the mtry was 40.

4.2. Hyperspectral Image Classification

4.2.1. Classification Accuracy Statistics

The classification results of high-frequency features showed significant improvement compared to using the original features (

Table 7. OA and Kappa coefficient of study area A and study area B. The order of features was sorted from high to low in OA.

Study Area A			Study Area B
Features	OA	Kappa Coefficients	Features	OA	Kappa Coefficients
haar_4_1234	0.769	0.736	haar_4_1234	0.885	0.862
haar_4_234	0.768	0.735	haar_3_123	0.884	0.861
haar_3_123	0.766	0.733	haar_4_234	0.880	0.856
haar_3_23	0.760	0.725	haar_3_23	0.878	0.853
db4_4_234	0.721	0.681	db2_4_234	0.870	0.844
db2_3_123	0.720	0.68	db2_4_1234	0.868	0.842
db2_4_1234	0.720	0.68	db10_4_1234	0.858	0.829
db2_4_234	0.718	0.677	db2_3_123	0.857	0.828
db2_3_23	0.717	0.676	db2_3_23	0.854	0.825
db10_4_1234	0.709	0.668	db8_4_1234	0.853	0.823
db10_4_234	0.709	0.667	db4_3_123	0.849	0.819
db4_4_1234	0.709	0.667	db10_4_234	0.849	0.819
db8_4_1234	0.700	0.658	db8_4_234	0.849	0.819
db4_3_23	0.700	0.657	db4_4_1234	0.849	0.819
db8_4_234	0.699	0.656	db4_3_23	0.848	0.818
db4_3_123	0.698	0.655	db4_4_234	0.848	0.817
db8_3_123	0.686	0.641	db8_3_123	0.839	0.807
db8_3_23	0.685	0.64	db10_3_123	0.836	0.803
original	0.683	0.637	db8_3_23	0.833	0.799
db10_3_123	0.679	0.633	db10_3_23	0.833	0.799
db10_3_23	0.662	0.614	original	0.813	0.776

). Means and standard deviations for 5-fold cross-validation of image spectral classification are shown in Figure A2 in Appendix A. For study area A, haar_4_1234 has the highest classification accuracy (OA: 0.769, Kappa coefficient: 0.736), with an 8.6% improvement over the original OA. For study area B, haar_4_1234 also exhibited the highest classification accuracy (OA: 0.885, Kappa coefficient: 0.862), with an improvement of 7.2% compared to the original OA. It is noteworthy that, for study area B, all the OAs of high-frequency features were higher than those of the original features. Combining the two study areas, the high-frequency features generated by the haar wavelet had high classification accuracy. The highest OAs were all from haar_4_1234.

For the highest F1-Score statistics, Pξγ and C₂wt achieved the highest scores (

Table 8. The highest value of F1-Score among the rock units on the image spectra in study area A using high-frequency features.

Rock Units	Highest F1-Score	Features (Highest F1-Score)	F1-Score of Haar_4_1234	Haar_4_1234 Ranking	Original F1-Score	Original F1-Score Ranking
C1x	0.745	haar_4_234	0.737	2	0.627	21
C1gd	0.720	haar_3_123	0.679	3	0.643	7
C1y	0.802	haar_3_123	0.795	3	0.665	21
Pξγ	0.907	haar_3_123	0.905	4	0.874	15
PQg	0.786	haar_4_1234	0.786	1	0.706	19
P1aer	0.651	haar_4_1234	0.651	1	0.555	20
Pγδ	0.813	haar_4_1234	0.813	1	0.721	13
Pγδπ	0.776	haar_4_1234	0.776	1	0.650	16

). Both of them had a classification accuracy of over 90%. Four types of rock units in study area A and three types of rock units in study area B (

Table 9. The highest value of F1-Score among the rock units on image spectra in study area B using high-frequency features.

Rock Units	Highest F1-Score	Features (Highest F1-Score)	F1-Score of Haar_4_1234	Haar_4_1234 Ranking	Original F1-Score	Original F1-Score Ranking
(E3-N1)t	0.875	haar_4_1234	0.875	1	0.796	21
Qp2W	0.866	haar_4_1234	0.866	1	0.780	11
Qp3X	0.881	haar_3_123	0.863	3	0.780	17
Cγ	0.886	db2_4_234	0.876	5	0.788	21
Cξγ	0.907	db8_4_1234	0.896	6	0.864	21
C2wt	0.933	haar_4_1234	0.933	1	0.872	21

) had the highest F1-Score from the haar_4_1234. The classification accuracy of igneous rocks was better than that of sedimentary rocks.

4.2.2. Intra-Class Variability

The image spectral curves and the wavelet-transformed curves of the rock unit samples were demonstrated in Figure 14 and Figure 15. Due to the lower spectral resolution of hyperspectral data, the distribution of high-frequency features is not as concentrated as in laboratory spectra. The intra-class SAM of image spectra showed a similar trend to laboratory spectra. It decreased with the use of high-frequency features (Figure 16, Figure 17, Figure 18 and Figure 19). For study area A, haar wavelets reduce intra-class SAM best. For study area B, the db2 wavelet reduces intra-class SAM best for most rock units.

4.2.3. Lithological Mapping

Combining the classification accuracies of image samples, a pixel-by-pixel DWT was applied to study areas using haar_4_1234 and implemented lithological mapping. The classifier for geological mapping was the RF algorithm. Ntree was set to 1000, and mtry was set to 17. For study area A (Figure 20) and study area B (Figure 21), the result maps had a high similarity with the geological map, and most of the rock units were correctly identified. The confusion matrices of the rock classification results for all pixels are shown in Table 10 and Table 11.

Study area A has some speckles in the result due to scour marks. Almost all of the scour marks were misclassified as other rock units. High-frequency features have improved the confusion of PQg with C₁y in the southeastern part of study area A. Compared to Figure 2A, 69.94% of the pixels were correctly classified, which was higher than the 63.76% using the original features. For PQg, 86.6% of the pixels were correctly classified. With the use of high-frequency features, more pixels were correctly classified for all rock units.

For Figure 21a, C₂wt was confused with Cξγ in the classification results (western part of study area B), and some of Cγ were misclassified as (E₃-N₁)t (central and eastern part of study area B). Figure 21b had less noise and better matched the boundaries of rock units with the geological map. It is clear that, consistent with the results of the original spectra, lithological mapping using wavelet high-frequency features had more pixels correctly classified. Compared to Figure 2B, 84.13% of the pixels are correctly classified, which is higher than the 77.34% using the original features. For (E₃-N₁)t, 89.2% of the pixels were correctly classified. With the use of high-frequency features, the percentage of correctly classified pixels was over 80% for all rock units.

Table 10. The confusion matrix of the rock classification results for all pixels in study area A. (The number before parentheses represents the predicted or actual percentage using high-frequency features of haar_4_1234. The number in parentheses represents the predicted or actual percentage using original features.) The ground truth came from the geological map (Figure 2A).

		Ground Truth (Percent)
		C1x	C1gd	C1y	Pξγ	PQg	P1aer	Pγδ	Pγδπ
Predicted (Percent)	C1x	80.1 (73.2)	0.4 (0.1)	7.3 (6.1)	0.8 (5.3)	0.7 (0.5)	2.6 (3.4)	0.6 (17.3)	16.6 (1.7)
	C1gd	0.4 (0.3)	80.2 (66.4)	5.1 (9.4)	2.2 (1.4)	0.3 (0.8)	1.1 (5.6)	14.2 (0.5)	2.1 (18.0)
	C1y	6.0 (1.2)	0.7 (12.3)	48.8 (43.1)	6.6 (4.9)	1.4 (1.6)	7.9 (9.0)	2.8 (3.8)	5.5 (7.2)
	Pξγ	1.7 (4.0)	2.3 (2.1)	9.4 (9.5)	76.4 (66.8)	8.2 (8.8)	7.8 (14.1)	8.0 (8.8)	1.6 (1.7)
	PQg	1.6 (0.3)	0.3 (1.9)	5.3 (5.7)	3.4 (8.2)	86.6 (85.0)	5.7 (6.3)	2.9 (3.1)	0.9 (1.1)
	P1aer	1.0 (1.8)	0.1 (2.8)	6.5 (7.1)	6.0 (5.9)	2.4 (1.7)	70.0 (50.5)	1.3 (3.8)	2.9 (5.8)
	Pγδ	0.9 (18.5)	15.1 (0.5)	11.2 (12.6)	4.7 (7.2)	0.4 (1.3)	4.0 (7.4)	70.0 (61.4)	3.8 (3.6)
	Pγδπ	8.3 (0.6)	1.0 (13.9)	6.4 (6.3)	0.1 (0.4)	0.0 (0.2)	0.9 (3.7)	0.3 (1.5)	66.7 (61.0)
		OA = 69.94% (63.76%)				Kappa = 0.62 (0.55)

Table 10. The confusion matrix of the rock classification results for all pixels in study area A. (The number before parentheses represents the predicted or actual percentage using high-frequency features of haar_4_1234. The number in parentheses represents the predicted or actual percentage using original features.) The ground truth came from the geological map (Figure 2A).

		Ground Truth (Percent)
		C1x	C1gd	C1y	Pξγ	PQg	P1aer	Pγδ	Pγδπ
Predicted (Percent)	C1x	80.1 (73.2)	0.4 (0.1)	7.3 (6.1)	0.8 (5.3)	0.7 (0.5)	2.6 (3.4)	0.6 (17.3)	16.6 (1.7)
	C1gd	0.4 (0.3)	80.2 (66.4)	5.1 (9.4)	2.2 (1.4)	0.3 (0.8)	1.1 (5.6)	14.2 (0.5)	2.1 (18.0)
	C1y	6.0 (1.2)	0.7 (12.3)	48.8 (43.1)	6.6 (4.9)	1.4 (1.6)	7.9 (9.0)	2.8 (3.8)	5.5 (7.2)
	Pξγ	1.7 (4.0)	2.3 (2.1)	9.4 (9.5)	76.4 (66.8)	8.2 (8.8)	7.8 (14.1)	8.0 (8.8)	1.6 (1.7)
	PQg	1.6 (0.3)	0.3 (1.9)	5.3 (5.7)	3.4 (8.2)	86.6 (85.0)	5.7 (6.3)	2.9 (3.1)	0.9 (1.1)
	P1aer	1.0 (1.8)	0.1 (2.8)	6.5 (7.1)	6.0 (5.9)	2.4 (1.7)	70.0 (50.5)	1.3 (3.8)	2.9 (5.8)
	Pγδ	0.9 (18.5)	15.1 (0.5)	11.2 (12.6)	4.7 (7.2)	0.4 (1.3)	4.0 (7.4)	70.0 (61.4)	3.8 (3.6)
	Pγδπ	8.3 (0.6)	1.0 (13.9)	6.4 (6.3)	0.1 (0.4)	0.0 (0.2)	0.9 (3.7)	0.3 (1.5)	66.7 (61.0)
		OA = 69.94% (63.76%)				Kappa = 0.62 (0.55)

Table 11. The confusion matrix of the rock classification results for all pixels in study area B. (The number before parentheses represents the predicted or actual percentage using high-frequency features of haar_4_1234. The number in parentheses represents the predicted or actual percentage using original features.) The ground truth came from the geological map (Figure 2B).

		Ground Truth (Percent)
		(E3-N1)t	Qp2W	Qp3X	Cγ	Cξγ	C2wt
Predicted (Percent)	(E3-N1)t	89.2 (79.8)	13.7 (16.6)	5.0 (7.2)	1.6 (5.8)	0.2 (0.1)	0.3 (0.4)
	Qp2W	8.6 (15.2)	81.8 (75.2)	4.4 (4.9)	0.8 (3.5)	0.8 (2.1)	0.4 (1.3)
	Qp3X	1.4 (1.8)	3.5 (4.7)	81.6 (71.8)	3.7 (3.6)	4.0 (10.2)	1.6 (3.5)
	Cγ	0.9 (3.2)	1.0 (3.3)	4.7 (9.5)	84.9 (79.8)	3.7 (4.3)	8.1 (7.8)
	Cξγ	0.0 (0.0)	0.0 (0.2)	3.8 (5.7)	1.3 (1.3)	87.0 (77.4)	3.0 (5.4)
	C2wt	0.0 (0.0)	0.0 (0.1)	0.5 (0.8)	7.8 (6.0)	4.3 (6.0)	86.5 (81.6)
		OA = 84.13% (77.34%)			Kappa = 0.80 (0.71)

Table 11. The confusion matrix of the rock classification results for all pixels in study area B. (The number before parentheses represents the predicted or actual percentage using high-frequency features of haar_4_1234. The number in parentheses represents the predicted or actual percentage using original features.) The ground truth came from the geological map (Figure 2B).

		Ground Truth (Percent)
		(E3-N1)t	Qp2W	Qp3X	Cγ	Cξγ	C2wt
Predicted (Percent)	(E3-N1)t	89.2 (79.8)	13.7 (16.6)	5.0 (7.2)	1.6 (5.8)	0.2 (0.1)	0.3 (0.4)
	Qp2W	8.6 (15.2)	81.8 (75.2)	4.4 (4.9)	0.8 (3.5)	0.8 (2.1)	0.4 (1.3)
	Qp3X	1.4 (1.8)	3.5 (4.7)	81.6 (71.8)	3.7 (3.6)	4.0 (10.2)	1.6 (3.5)
	Cγ	0.9 (3.2)	1.0 (3.3)	4.7 (9.5)	84.9 (79.8)	3.7 (4.3)	8.1 (7.8)
	Cξγ	0.0 (0.0)	0.0 (0.2)	3.8 (5.7)	1.3 (1.3)	87.0 (77.4)	3.0 (5.4)
	C2wt	0.0 (0.0)	0.0 (0.1)	0.5 (0.8)	7.8 (6.0)	4.3 (6.0)	86.5 (81.6)
		OA = 84.13% (77.34%)			Kappa = 0.80 (0.71)

4.3. Relationship between OA and Intra-Class Variability

Figure 22a shows the scatterplot of OA and the mean of SAM, and Figure 22b shows the scatterplot of F1-Score and the mean of SAM. We calculated the Pearson correlation coefficient between OA, or F1-Score, and the mean of intra-class SAM (

Table 12. Pearson correlation coefficient between the mean intra-class SAM and OA.

Research Target	Pearson Correlation Coefficient
Laboratory spectra	−0.734
Image spectra (study area A)	−0.588
Image spectra (study area B)	−0.751

and

Table 13. Pearson correlation coefficient between the mean intra-class SAM and F1-Score.

Laboratory Spectra		Study Area A		Study Area B
Rock	Pearson Correlation Coefficient	Rock Unit	Pearson Correlation Coefficient	Rock Unit	Pearson Correlation Coefficient
Dolostone	−0.971	C1x	−0.849	(E3-N1)t	−0.600
Andesite	−0.202	C1gd	0.197	Qp2W	−0.183
Tuff	−0.857	C1y	−0.610	Qp3X	−0.583
Limestone	−0.818	Pξγ	−0.638	Cγ	−0.973
Sandstone	0.101	PQg	−0.600	Cξγ	−0.827
Granite	−0.535	P1aer	−0.700	C2wt	−0.889
		Pγδ	−0.163
		Pγδπ	−0.611

). The values of SAM are from Figure 11, Figure 16 and Figure 18. For both laboratory spectra and image spectra, there was a negative correlation between intra-class SAM and OA. As the intra-class SAM decreased, there was a tendency for OA to increase. For study area A, the Pearson correlation coefficient between the mean intra-class SAM and OA shows a weak correlation. For dolostone, the Pearson correlation coefficient between the mean intra-class SAM and F1-Score showed a strong correlation at −0.971. This may indicate that the most important factor affecting the accuracy of dolostone classification is intra-class variability. For sandstone and C₁gd, F1-Score and SAM showed a weak positive correlation. This suggests that intra-class variability may not be the cause of classification accuracy for these two rocks (rock units).

5. Discussion

Lithological mapping using remote sensing technology presents significant challenges. This work applied the high-frequency components of DWT to hyperspectral lithological classification. The high-frequency features reduced the intra-class variability of rock spectra and highlighted the bands that were beneficial for rock classification.

5.1. Laboratory Spectral Classification

The high-frequency features highlight the differences between rock samples. Although the inter-class separability decreases in most bands, the dominant bands for rock classification are highlighted. The RF classifier has advantages in processing high-dimensional data, makes feature reduction unnecessary, and makes the DWT-RF method highly generalizable. The tuff samples include breccia-crystalline clastic tuff, andesite tuff, andesite-bearing breccia-crystalline clastic tuff, etc. (Figure 23). The abundance of subclasses in the samples may affect the classification accuracy.

In our study, we only performed wavelet decompositions at three or four levels. As the number of decomposition levels increases, more high-frequency information is extracted, and the time for wavelet decomposition and reconstruction increases. Wavelet transform only decomposes low-frequency coefficients, so higher-level low-frequency coefficients may not contain useful information for classification. Wavelet packet decomposition is a further optimization of wavelet decomposition. The wavelet packet decomposition decomposes not only low-frequency sub-bands but also high-frequency sub-bands at each level of signal decomposition. We consider using the wavelet packet transform to extract more features to improve the classification in the future.

5.2. Hyperspectral Image Classification

Lithological mapping using GF-5 AHSI data obtained clear boundaries for rock units. If visual interpretation is assisted after classification, the boundaries can be directly used for producing geological maps. The image spectra are considered more suitable as samples for lithological mapping, and laboratory spectra are somewhat different from image spectra due to the influence of rock morphology [56]. C₁y has the poorest classification accuracy of all the rock units, with only 48.8% of the image elements correctly classified, even after using high-frequency features. In Figure 14e, the image spectra of sample A have high intra-class variability, with spectral intensities varying by more than 0.2. The high intra-class variability in image spectra may be due to rock fragmentation or weathering [57]. In addition, the black powder formed via coal weathering also interferes with lithology discrimination (Figure 24) [44]. Unlike handheld spectrometers, hyperspectral sensors acquire spectra of rock weathering surfaces and may mix multiple types of rocks in one pixel [58].

5.3. Limitations and Strengths of This Study

The DWT-RF method demonstrates good classification ability in both laboratory spectra and image spectra, indicating that subtle differences between rocks are captured by the high-frequency features. OA increased for all fourteen types of rock units, and high-frequency features consistently improved the effectiveness of lithological discrimination. In the laboratory spectral classification of rock samples, granite and dolostone were better identified, but andesite had an F1-Score of only 0.418. After using the high-frequency features, the boundaries of Pξγ in the southern part and C₁x in the northwestern part of study area A were well extracted. Pγδπ and P₁aer in the northern part of study area A still had pixel confusion after the use of high-frequency features. Study area B with less surface relief had better classification results.

Currently, this method can only be used for geological mapping in arid or semi-arid areas with exposed rock outcrops. In vegetation-covered areas, the image spectrum is a mixture of vegetation and rocks, which is different from the laboratory spectrum [59]. Hewson et al. [60] used a threshold of 0.4 to mask the vegetation before generating the mineral composition map. A variety of rocks are exposed in the area where the hand specimens were collected, and many of them, such as dolostone and andesite, were not found in the lithological mapping area. Unfortunately, the area where the hand-specimen rocks were collected was heavily vegetated, with few samples with no or little vegetation cover. The area chosen for lithological mapping is the Eastern Tianshan region, which is a good area for geological investigations because there is little vegetation cover. The classification of the laboratory spectra and the classification of the image spectra were tested separately, so we chose the two most suitable areas. When DWT has a positive effect on both the hand-specimen spectra and image spectra, methods are considered essentially feasible. If laboratory spectra could assist in geological mapping, this would increase the accuracy of lithological mapping. Establishing the relationship between vegetation spectra and underlying rock spectra enables geological mapping in vegetation-covered areas, which is beneficial for regional geological mapping. More efforts are needed in the future to improve classification accuracy and reduce noise in hyperspectral data. High-frequency features are susceptible to noise, and filtering may lose information useful for classification. Data fusion from multiple sources may be a good choice, which helps to reduce the interference of noise. In addition, SAM is sometimes sensitive to illumination variations. Finding more efficient classifiers and more accurate spectral similarity metric indices is important for geological mapping.

6. Conclusions

The purpose of this study is to discuss the ability of DWT to improve rock classification. Based on laboratory spectra and GF-5 AHSI data, it can be concluded that high-frequency features after DWT reduce the intra-class variability of all rocks and rock units. For both laboratory spectra and image spectra, four-level DWT using the haar wavelet gives the best classification results. The F1-Score of dolostone improved from 0.464 to 0.689 after DWT. For the classification of rock units, after using high-frequency features, the F1-Score of Pξγ is 0.907, and the F1-Score of C₂wt is 0.933. The classification accuracy is influenced by the MF, decomposition levels, and reconstruction methods. MF with smaller vanishing moments can better improve classification accuracy. After DWT, the intra-class SAM reduces, and the mean of SAM is negatively correlated with the classification accuracy.

More strategies need to be used to reduce the interference of noise, which is important for hyperspectral remote sensing geology. Once the relationship between vegetation and underlying rocks is determined, regional geological mapping will be possible.