The Feasibility of Shadowed Image Restoration Using the Synthetic Aperture Focusing Technique

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At present, there is no relevant research which explores possible lesions in ultrasound images that may exist in acoustic shadow; only a differential diagnosis can be made. This current work addresses the use of a reliable posterior restoration algorithm for possible acoustic shadowed lesions. Our results reveal the potential for a SAFT-based restorative application that may provide diagnostic information in medical sonography.

Abstract

The phenomenon of acoustic shadowing on ultrasonography is characterized by an echo signal void behind structures that strongly absorb or reflect ultrasonic energy. In medical ultrasonography, once the ultrasound energy is shielded, acoustic shadowing makes it difficult to create an image, leading to misinterpretations and obscure diagnoses. Hence, instead of dealing with the defocused problem encountered in an ultrasound scan (US), this current research focuses on revealing the existence of an acoustically shadowed target (or a potential lesion) using a well-known restoration algorithm, i.e., the synthetic aperture focusing technique (SAFT). To demonstrate the effects of an acoustic shadow on an ultrasound scan (US), a forward model study is carried out. In laboratory manipulations, a purposely designed physical model is created and then scanned using B-mode and pitch/catch arrangements to carry out shadowed and shadow-free scans in a water tank. Thereafter, making use of a delay-and-sum (DAS) operation, the echo signals are processed by the synthetic aperture focusing technique (SAFT) to perform image restoration. The results of the restoration process show that the SAFT algorithm performs well with respect to directional shadowing. Once the target or lesion is positioned in a total anechoic zone, or even in a multi-channel scan, it will fail.

1. Introduction

The advantageous properties of ultrasound scanning (US), such as non-invasiveness and non-radiation, are widely used in medical diagnosis [1,2,3]. US uses the interaction of high-frequency acoustic energy in a specimen to produce an original image that reveals tissues inside the human body. High-frequency (1 to 20 MHz) sound energy is transmitted into a specimen by an ultrasound machine in the form of multiple pulses, and the echoes are relayed on a monitor and form a two-dimensional image. However, the US still suffers from limitations in resolution, contrast, and signal-to-noise ratio (SNR), and is not free from artefacts [4]. Acoustic shadowing, a feature of ultrasound images, is one of the artefacts inherent in US imaging.

Acoustic shadowing is detected as an ultrasonic manifestation. Occurrences of anechoic zones caused by acoustic shadowing are devoid of echo and fail to render reliable images in US [3,5]. In response to acoustic shadowing, the anechoic zone displays as a dark area, e.g., due to the echogenic appearance of tissue posterior to kidney stones, gallstones, benign or malignant tumors, foreign bodies, complex sclerosing lesions, postoperative scars, fibrous or dense breast tissue, etc. [6,7,8,9]. Hence, in a traditional sonographic examination, acoustic shadowing is often used to explore possible relevant differential diagnoses rather than the further use of ultrasound to diagnose the shadowed lesions [10].

In medical sonography, a shadowed tissue induced by acoustic shadowing cannot be revealed by increasing the power or gain of the ultrasound machine. However, due to the directionality of acoustic shadowing and the acoustic radiation (beam) pattern, a shadowed target that is echo-free at a specific scan position can be echoed in other scan positions in a multi-channel scan [11,12]. Hence, it is critical and worthwhile for us to overcome the artefacts resulting from acoustic shadowing that degrade the attainable ultrasonic image. Typically, a posterior restoration process is employed to reconstruct the original image from observations.

Nowadays, restoration techniques are significantly advanced, owing to the development of digital processes [13,14]. With the heuristic principle of signal superposition via constructive interference, the synthetic aperture focusing technique (SAFT) algorithm allows each point within the target to be focused upon by mathematically simulating the action of a lens specifically formed for imaging the target inside the structure. The efficiencies and easy manipulation make SAFT one of the most popular processing technologies used to improve image quality and maximize the resolution from acquired echo signals. SAFT is proposed to facilitate the original image restoration by trying to “undo” the effects of acoustic shadowing on an ultrasonic image [15,16].

The acoustic shadowing encountered in the sonographic examination is often used to explore possible relevant differential diagnoses, rather than to reveal the shadowed lesions [7,17]. In this study, a forward model study is carried out to demonstrate the phenomenon of acoustic shadowing in US and to perform data acquisition. In the posterior stage of image restoration, the acquired data are then processed by SAFT. It is hoped that a potential target hidden under acoustic shadowing can be revealed from restored images. The remainder of this article is therefore organized as follows. First, the laboratory manipulation designed to facilitate the acoustic shadowing experiment is introduced. Subsequently, the theoretical background of SAFT, which is used to perform shadowed image restoration, is briefly described, and the results of laboratory work are presented. Finally, the applications and limitations of the restoration algorithm are addressed in the discussions and conclusions.

2. Experimental Setup

Obscuring by acoustic shadow in an ultrasound image is somewhat similar to the phenomenon of an eclipse, whereby one object to be imaged is shielded by the shadow of another. A forward model study is carried out to demonstrate the effects of acoustic shadowing on the ultrasound image.

2.1. Physical Model

The physical model created to perform this shadowing scan consists of a skew driver rod and seven fishing lines (Figure 1a). The rod (T_OBS), 5.5 mm in diameter, is used as an obstacle for three fishing lines (T₁, T₂, and T₃). The other four fishing lines (T₄, T₅, T_6, and T₇) are used to serve as a comparison. The diameter of the fishing line (T_N) is 0.7 mm. Taking gallstone ultrasound as an example, T₁, T₂, and T₃ can be considered to be small gallstones shadowed by a big one, T_OBS. To create the shadowing effect and, as a contrast, T_OBS, T₁, T₂, T₃, T₄, T₅, T₆, and T₇, respectively, are aligned inline. For this purpose, T₁, T₂, and T₃ are positioned behind T_OBS to obtain a shadowed image for the scan position SP_OBS. Additionally, SP_FR, T₄, T₄, T₅, and T₇ are also aligned inline for an obstacle-free scan. Both of the alignment lines are perpendicular to the scan surface (Figure 1b). The pink dot-line shown in Figure 1 indicates the scan line. SP_OBS and SP_FR located on the dot-line are two specific scan positions to perform shadowed and shadow-free scans.

2.2. Laboratory Manipulation

For the process of data acquisition, the model is soaked into a water tank to perform an immersed scan (Figure 1b). The P-wave velocity in water is premeasured as 1450 m/s. The active transducer used to facilitate our laboratory manipulation is an Olympus (V204-RM 2.25 MHz/6 mm) [18]. The dominant frequency of the active transducer thus makes the wavelength of the propagating P-wave 0.6 mm; hence, the dimensions of TOSB and TN are approximately ten times and equal to the dominant wavelength, respectively.

For the process of data acquisition, a PANAMETRICS 5058 pulser–receiver is adjusted to be either in single probe or a pulse/echo mode to perform a B-mode scan and a pitch/catch scan, generate an electric pulse, receive the electric signal, and synchronize (Sync) the digital oscilloscope (Tektronix DPO3034) [19,20]. The digitized radio frequency (RF) signal is then downloaded from the digital oscilloscope via a general-purpose interface bus (GPIB) and IEEE-488 communication to a personal computer for further processing. When the digitized echo signal is created, the transducer is automatically moved to the next location.

2.3. Restoration Algorithm-Synthetic Aperture Focusing Technique (SAFT)

In US, data are acquired simultaneously from all directions over a number of emissions. Echo signals are recorded independently by individual elements of the receive sub-aperture. However, signals shown in the ultrasound image may not indicate the real position of where the acquired echoes originated. To access reliable inside information of a medium from an ultrasound image, a restoration operation has often been applied to the acquired data to reconstruct the interior structure. Among all kinds of existing restoration algorithms, SAFT is the one that has been around for a long time and is extensively used to achieve echo energy refocusing and image resolution enhancement. In the process of SAFT, the relationship between the echo signals of N sensors disposed of inline (multi-channel scans) is calculated, and thereafter a defocused image is reconstructed by summing all demodulated input echo signals [21,22,23,24,25]. SAFT can be performed either in the image domain or the frequency domain to accommodate image reconstruction. In the subsequent stage of image processing in this work, SAFT is performed in the time domain using delay-and-sum (DAS) processing to restore ultrasonic images obtained from B- and pitch/catch scans under acoustic shadowing.

A brief description of applying SAFT to facilitate the reveal of a shadowed image is shown in Figure 2. It is assumed that a point diffractor (T) is immersed in water, and a sensor emitting a spherical wave is used to obtain a B-scan image of the diffractor (T) (Figure 2). By summing the delayed time traces of the B-scan image [SPi(x ± I × dx, t + dt_i)], the reconstructed image [SP(x, t)] processed by the SAFT is given by

$$\mathrm{T}=SP\left(x, t\right)={{\displaystyle \sum }}_{i=-n}^{n}S{P}_i\left(x\pm i\times dx,t+d{t}_i\right),$$

(1)

$$d{t}_i=\sqrt{{\left(\frac{2i\times dx}{V}\right)}^2+t^2}-t,$$

(2)

where dx is the successive lateral scanning interval; t is the vertical two-way propagation time of the pulse from the probe to the flaw and back; and V is the speed of sound in water. For scanning position x, dt_i in (1) is the time delay for the successive scanline, i × dx, with respect to the point diffractor (T); i = ±n; the maximum lateral distance at which the echo signals diffracted from the diffractor (T) can be detected by the sensor.

3. Results

3.1. Synthetic Simulation

Taking the spreading attenuation into consideration, a synthetic profile of the pitch/catch scan obtained from the model is computed using the Levin equation [26]. At a sampling interval of 16 ns, a zero-phase Ricker wavelet is used to compute the synthetic profile using FORTRAN language. The velocity used is the same as the modeling material, i.e., 1450 m/s. Following the practical operation, the spacing interval of two successive traces is fixed at 2 mm. In the following paragraphs, the synthetic profile is used to assist image interpretation and serve as test data to evaluate the performance of SAFT in image restoration. Figure 3a shows the synthetic profile which is computed, based on the theoretical echo paths that respond from the “eight targets”, i.e., the relative positions of T_OBS and T_N inside the created model. According to point diffraction theory, there should be eight hyperbolic trajectories showing up in the synthetic profiles, with the targets as the apexes. When the scan positions (SPs) move or are close to the projection of T_OBS, echo signals around the vicinity of the apexes T₁, T_2, and T₃ are purposely muted to simulate and demonstrate the shadowed images in an anechoic zone (Figure 3a). In the synthetic and the following images, echo signals are displayed using a linear grayscale from black (the smallest) to white (the largest).

The synthetic profile is SAFT-processed; Figure 3b shows the output images of restoration. Even though part of the echo signals is purposely muted in the incomplete trajectories, T₁, T₂, and T₃ respond to the acoustic shadow. All the hyperbolic trajectories shown in Figure 3a are successfully refocused as eight spots and repositioned in Figure 3b. The apex positions of T_OBS and T₄ that show up at 40.0 μs and 43.6 μs in Figure 3a are shifted upward to 37.6 μs and 41.3 μs, respectively, in Figure 3b, in response to the SAFT process. In other words, the events of T_OBS and T₄ are not only successfully restored, but also relocated to a new position.

3.2. Experimental Results

To facilitate the objective of this study, the created model is scanned using B-mode and pitch/catch arrangements. For the pitch/catch mode scan, the spacing interval of two active transducers is fixed at 20 mm. The pink line shown in Figure 1 indicates the scan that runs perpendicular to the orientations of the rod of the skew driver and fishing lines. The scan line extends from 30 mm on the left-hand side of SP_OBS to 30 mm on the right-hand side of SP_FR (Figure 1b). Hence, the total length of the scan line is 90 mm. The offset interval in between each successive scan is 2 mm. In total, 46 observations are performed in a complete scan. Each observation consists of 2500 points sampled at an interval of 8 ns, which equates to a time frame of 20 μs.

Figure 4a shows the result of the B-mode scan. Though the synthetic profile shown in Figure 3a is computed for the pitch/catch scan, it can still be used to assist in identifying images obtained from the B-mode scan (Figure 4a). Once a comparison is made between Figure 3a and Figure 4a, it can be identified that their echo signals observed at 41.3 μs and 77.6 μs at SP_OBS in Figure 4a came from T_OBS and T₃, though the echo strength is weak for T₃. In terms of the eclipse, T₁, and T₂, which fall within the umbra area and at the intersection of umbra and antumbra of the echo field caused by T_OBS, fail to be imaged. At SP_FR, fishing lines labeled T₄, T₅, T₆, and T₇ are detected at 40.8 μs, 48.7 μs, 61.1 μs, and 78.1 μs. In addition, a question-marked event is observed at the lower center of Figure 4a, and is identified as a multiple-echo of T_OBS. Once the original observations (Figure 4a) are SAFT-processed, Figure 4b shows the output. In Figure 4b, the images of T_OBS, T₃, T₄, T₅, T₆, and T₇ are all well restored at the proper positions. The multiple echo, shown by a red question mark in Figure 4a, which comes from T_OBS, is gone.

Figure 5a shows the result of the pitch/catch scan. In Figure 5a, the echoes from T_OBS and T₃ are detected at 40.1 μs and 79.8 μs at SP_OBS, respectively. Out of T_OBS and T₃, one more echo is detected at 63.3 μs. Referring to the synthetic profile (Figure 3a), this new echo is identified as T₂. In addition, echoes coming from T₄, T₅, T₆, and T₇ are individually observed at 43.5 μs, 53.5 μs, 63.6 μs, and 81.1 μs at SP_FR. However, limited by the overlap of the beam divergence angle, the trajectories of imaged targets show up as an incomplete hyperbolae in the acquired scan [27,28]. Thereafter, the original observations are SAFT-processed. Once again, the intersections of dark blue dashed lines and pink dashed lines indicate the original and SAFT-processed images of T_OBS and T₄, respectively. In Figure 5b, it can be seen the original echo image shown in the raw data, i.e., Figure 5a, is not just restored but also properly repositioned.

To acquire more details into the performance of SAFT in shadowed image restoration, the acquired echo signals and SAFT-processed data are Hilbert-transformed to perform echo strength analysis [29]. The outputs of echo strength analysis are normalized using the maximum echo strength of the raw data and SAFT-processed events at the specific scan positions, i.e., SP_OBS. In Figure 6, the normalized echo strengths of observed echoes (raw data; in dark blue) and restored images (in pink) along the axial direction for the B-mode scan and pitch/catch mode scan are displayed. For the B-mode scan (Figure 6a), it can be seen that the observed events are refocused at the positions where the targets are imaged. For the pitch/catch scan (Figure 6b), the performance of the SAFT process in image restoration becomes more obvious. The images of the detected targets are not just refocused but also repositioned. Although the background noise comes with the restoration process, the image resolution is enhanced. Detailed information of observed (raw) data and SAFT-processed data are tabularized in

Table 1. Details of the original observations (raw data) and SAFT-processed data for the B-mode scan (Figure 3). Numbers shown below the targets (T_OBS and T_N) are the depths of the centers and the tops of the relative holes (center/top). Numbers above the slash of relative imaged echoes show the information of original observations and those below the slash are obtained from the results of the SAFT process.

B-Mode Scan
SPOBS		SPFR
TOBS 30.0/27.25 (mm)	41.3/37.5 (μs) 27.5/27.2 (mm)	40.8/40.7 (μs) 29.6/29.5 (mm)	T4 30.0/29.65 (mm)
T1 38.0/37.65 (mm)		48.7/48.7 (μs) 36.8/36.8 (mm)	T5 38.0/37.65 (mm)
T2 46/45.65 (mm)		61.1/61.1 (μs) 44.3/44.3 (mm)	T6 46/45.65 (mm)
T3 58/57.65 (mm)	77.6/80.0 (μs) 56.3/58.0 (mm)	78.1/80.2 (μs) 56.7/58.1 (mm)	T7 58/57.65 (mm)

and

Table 2. Details of the original observations (raw data) and SAFT-processed data for the pitch/catch mode scan (Figure 4). Numbers shown below the targets (T_OBS and T_N) are the depths of the centers and the tops of the relative holes (center/top). Numbers above the slash of relative imaged echoes show the information of original observations and those below the slash are obtained from the results of the SAFT process.

Pitch/Catch Scan
SPOBS		SPFR
TOBS 30.0/27.25 (mm)	40.1/37.7 (μs) 29.1/27.3 (mm)	43.5/41.7 (μs) 31.6/30.2 (mm)	T4 30.0/27.25 (mm)
T1 38.0/37.65 (mm)		53.5/51.6 (μs) 38.8/37.4 (mm)	T5 38.0/37.65 (mm)
T2 46/45.65 (mm)	63.3/60.8 (μs) 46.1/44.1 (mm)	63.6/61.9 (μs) 46.1/44.9 (mm)	T6 46/45.65 (mm)
T3 58/57.65 (mm)	79.8/77.5 (μs) 57.8/56.2 (mm)	81.1/81.0 (μs) 5.8/58.8 (mm)	T7 58/57.65 (mm)

, respectively.

4. Discussion

At present, there is no relevant research which explores the potential lesions lying in acoustic shadow; a differential diagnosis is the best that can be done [7,17]. This current research is the first use of SAFT to reveal the existence of an object that is in the acoustic shadow. In addition, to simulate human tissue, this study uses water as the medium and monofilament to perform immersed scans. The low acoustic impedance contrast between water and the monofilament line thus degrades the laboratory data. However, satisfying results are still being achieved, providing effective information for the future development of ultrasonic detection methods.

Before directly applying SAFT to the laboratory data, a synthetic pitch/catch scan profile is computed, based on point reflection/diffraction theory. Eight targets of different spatial positions are purposely arranged. In Figure 3a, the theoretical echo signals that can be detected from the created targets show up as eight hyperbolic trajectories. To simulate a shadowed image, part of the echo signals from three of the targets, i.e., T₁, T₂, and T₃, are purposely silenced. Once the synthetic image is SAFT-processed, Figure 3b demonstrates the output. In Figure 3b, it can be seen that the original images of all created targets, T_OBS and T_N, are perfectly reconstructed and repositioned. Restoration is also expected for the shadowed targets. The technique requires a partial or distorted signal for the restoration algorithm to reliably reconstruct the shadowed object. In particular, a sufficient amount of data is required to achieve a satisfactory restoration job. In other words, a degraded restoration of an image can be achieved as a result of incomplete echo signals.

In the immersed experiments, the created model is scanned by B-mode and then pitch/catch arrangements. For clarity, the theoretical echo paths for B-mode and pitch/catch scans are depicted and shown in Figure 7. In Figure 7a, we can see that when the scan is performed at SP_OBS, targets (T₁, T₂, and T₃) that are located behind the obstacle (T_OBS) might not be echoed and become invisible in the original scan. Once the scanning is performed away from SP_OBS, e.g., at SP_FR, the shadowed targets can be partly echoed. In the essence of image restoration, an original image is restored by calculating the relationship between the echo signals of N sensors disposed of inline (multi-channel scans) and summing up all demodulated echo signals detected (Figure 3).

In the practical operation of the SAFT process, the performance of image restoration is also highly dominated by the beam pattern, i.e., the divergence angle of the active sensor. The beam pattern is determined by factors such as the velocity of the medium to be scanned, the frequency and size of the active sensor, and the acoustic phase characteristics of the vibrating surface [27,28], possibly due to the effects of wavefront healing or whether the created model is scanned using B-mode or pitch/catch. The targets positioned behind T₄, i.e., T₅, T₆, and T₇, are all echoed in the scan images (Figure 4a and Figure 5a) [30]. The radiation angle of an active sensor is proportional to the sound wave in the medium. In our immersed scan, the P-wave propagates with a slower velocity in water and limits the divergence angle of the active sensor. The limited divergence angle thus narrows the overlap of the emitted beam and reflected beam; therefore, the acquired trajectories originated by reflection/diffraction are incomplete (Figure 5a). Regardless of the scanning arrangements, target T₁ always fails to be echoed and restored. Our laboratory results thus show that image restoration cannot happen out of nothing. Once a target to be imaged falls within the anechoic zone, nothing can be done to restore the original image.

5. Conclusions

Medical diagnosis is only as good as the diagnostic tools used. In sonographic diagnosis, the US can only detect lesions from the anterior; it is rarely used to detect human soft tissue lesions in circumferential 360 degrees. The use of US could fail to provide reliable diagnoses of tumors located either between the heterotopic ossification and joint, or eyeball tumors, due to the skull barrier behind the eyeball, causing acoustic shadowing. Making use of a forward model study, the phenomena of acoustic shadowing were demonstrated, and the digitized echo signals were obtained. Acquired data were processed by a restoration technique, i.e., SAFT. Restoration output commends a target that is imaged under acoustic shadowing could be conditionally revealed and encourages the feasibility of revealing the existence of a potential lesion behind the larger and harder tissues or lesions. However, there are some limitations. Unless a target to be imaged can be partly echoed in the multi-channel scans, a shadowed image will not be unveiled. In other words, only a shadowed lesion that can be echoed using ultrasonography could be diagnosed, which is theoretically reasonable. Once the targets of potential lesions are positioned in a totally anechoic area, i.e., umbra in eclipse, the scanning task will fail.