**1. Introduction**

Optical remote sensing data become available with an increased temporal and spatial resolution, in particular since the Copernicus program launched the Sentinel-2A and Sentinel-2B satellites in 2015 and 2017 [1]. This has opened new opportunities for monitoring vegetation dynamics up to the local scale. Inspecting changes of the spectral signature of vegetation over time can be used to, e.g., monitor crop growth [2], forest degradation [3], and grassland use intensity [4].

However, optical remote sensing is highly affected by atmospheric perturbations, which cause both gaps and noise in the time series. In [5–7], the problem of gaps is addressed by data assimilation from multiple sensors with similar characteristics. Gaps can also be filled by combining data from sensors with different characteristics such as optical and synthetic aperture radar (SAR) sensors [8]. More recently, machine learning models have been introduced to fill gaps by predicting the missing values, e.g., from SAR data [9]. In [10], Landsat and Sentinel-2 surface reflectance have been fused using deep learning techniques. A more simple approach is to fill gaps in the time series via interpolation of clear observations [11]. This avoids issues with data harmonization and co-registration between different sensors [12]. Noise in the time series are due to undetected clouds or other variations in atmospheric conditions such as aerosol concentration. A subsequent noise reduction filter is therefore often applied [13,14]. One of the difficulties in designing such a filter is the trade-off between the ability to reduce unwanted noise and the retention of the relevant changes. Low-pass or smoothing filters are effective at reducing noise in time series with high-frequency fluctuations, but can also affect seasonal vegetation changes. Edges in the vegetation signature risk to be blurred by such filters. These edges

**Citation:** Kempeneers, P.; Claverie, M.; d'Andrimont, R. Using a Vegetation Index as a Proxy for Reliability in Surface Reflectance Time Series Reconstruction (RTSR). *Remote Sens.* **2023**, *15*, 2303. https:// doi.org/10.3390/rs15092303

Academic Editor: Lenio Soares Galvao

Received: 19 January 2023 Revised: 20 April 2023 Accepted: 24 April 2023 Published: 27 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

are useful features for agriculture applications that study crop harvest practices and rely on, e.g., the identification of the start and end of the growing season [15,16]. Furthermore, for the detection of disruptive events such as land cover change, fire, and floods, the design of the smoothing filter requires special care [13].

Within the context of time-series reconstruction, vegetation indices such as the normalized difference vegetation index (NDVI [17]) have the interesting property that they are usually depressed in cloudy or poor atmospheric conditions [18]. In [19], NDVI was analyzed under different observation conditions. The authors demonstrated that the NDVI values for all land cover types increase with lower aerosol concentrations, near-nadir viewing and high solar illumination. It was therefore concluded that "the best possible pixel value for a particular location is achieved by choosing the highest pixel value from multi temporal data". High NDVI values can therefore be assumed to be more trustworthy than low NDVI values. This has been successfully used to reconstruct time series of NDVI by approaching the upper NDVI envelope via an iterative process [20–22]. The maximum NDVI composite is also based on this property. It creates a single noise-free image from a series of images by selecting the acquisition with the maximum NDVI value [19,23,24]. An overview of techniques to reduce noise of NDVI time series is provided in [25].

For some applications, a multi-variate analysis is preferred over a single index. On the use of time series for detecting land disturbance in [26], it was found that the combined use of spectral bands was better than using a single spectral band or index. Furthermore, in the context of analysis-ready data (ARD [27]), the reconstruction of surface reflectance time series is important. A fill-and-fit approach was followed in [28], where missing pixels are filled with a clear observation in the same or a temporally close image. The selection of the clear observation is based on a similarity measure. A subsequent fitting, based on a (linear or non-linear) harmonic model, then reconstructs the time series. In [29], both NDVI and surface reflectance time series from Sentinel-2 were reconstructed using the penalized least-square regression based on the discrete cosine transform (DCT-PLS). Surface reflectance was also reconstructed in [30], by incorporating the upper envelopes of the time-series vegetation index as constraint conditions. The authors reconstructed surfacereflectance time series for MODIS [30] and advanced very high resolution radiometer (AVHRR) data [31]. Recently, a dynamic temporal smoothing (DTS [32]) method was proposed that can also be applied to surface reflectance values. Although the authors focus in their paper on the two-band enhanced vegetation index (EVI2 [33]), the code presented in [32] can be applied to time series of spectral reflectance. However, the DTS algorithm presented in [33] involves an adjustment of the smoothed value of the vegetation index under study (i.e., EVI2) to the upper envelope of the time series. The assumption that relatively high values correspond to trustworthy observations does not hold for surface reflectance in general. On the contrary, the reflectance value in the visible and near infrared part of the electromagnetic spectrum typically increases for cloud covered pixels.

In this study, a new surface Reflectance Time Series Reconstruction (RTSR) method is proposed for vegetation monitoring. It adjusts the smoothed values, similar to existing reconstruction methods that act on vegetation indices. It hereby decouples the vegetation index as a proxy for reliability from the time series of the reflectance values to be reconstructed. Unlike existing methods that let the smoothed time series approach the upper envelope, the surface-reflectance times series here approaches the trustworthy observations. The remaining sections are structured as follows. In Section 2, the materials are covered with a description of the test sites and remote-sensing time series. The RTSR method is described in Section 3 as well the as the evaluation procedure. Results and the evaluation are presented in Section 4. A discussion with limitations of the proposed method is described in Section 5. Conclusions are drawn in Section 6.
