## 3 Experiments
### Tests on Synthetic Images  
To validate the effectiveness of the proposed strategy, we conducted our tests on synthetic images. For quantitative comparison, we first added speckle noise to the clean images by employing the synthetic speckle noise model [12] on a synthetic image, as shown in Figure 5a. As in [PERSON] et al. [14],  
Figure 4: The reconstructed images with different superpixel sizes (in pixel). From (**a–d**), the superpixel sizes are 3, 5, 7, and 9, respectively.  
the added noise is a multiplicative Gaussian \(N(0,\delta_{s}^{2})\) noise, where \(\delta_{s}\) controls the noise level, and we set the noise level as \(\delta_{s}=\{0.15;0.2;0.25;0.3\}\) on the test synthetic image. Figure 5b illustrates the corresponding noisy image with \(\delta_{s}=0.3\). In addition, we also adopted the Field II toolbox [27; 28] to add speckle noise to another clean image, as shown in Figure 5c, and the corresponding image with speckle noise is shown in Figure 5d. The Field II toolbox is a program for simulating the image of ultrasound scanners. It can calculate pulsed pressure fields, and can also handle continuous wave and pulse-echo cases [27; 28]. As we can see, the generated Field II image seems very close to a real ultrasound image.  
We mainly compared our method with two state-of-the-art non-local despeckling methods, the optimized Bayesian non local means filter (OBNLM) [29] and the non-local low-rank method proposed by [PERSON] et al. [14]. As our method employs the superpixel version of bilateral filtering, we also compared the processing results with those given by the local method of bilateral filtering [6] with fine-tuned parameters, as a baseline. We adopted two commonly used metrics, peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [30], to quantitatively compare the performance of our method against others. PSNR is an image quality measure after some modification to the image is done, and SSIM is used for measuring the structural similarity between two images. Both PSNR and SSIM are full reference metrics, which means the measurement of image quality is based on an initial distortion-free image as a reference. Generally, for the speckle reducing task, higher values of PSNR and SSIM indicate better performance.  
From the PSNR and SSIM values listed in Tables 1 and 2, our method performed slightly worse than the method proposed by [PERSON] et al. [14] and/or OBNLM [29] on the synthetic image in Figure 5b, in which the noise was added using the multiplicative Gaussian model, but performed remarkably better on the synthetic image in Figure 5d, in which the speckle noise was added using the Field II toolbox [27; 28]. We think the observation that our method performs better on the Field II-generated image is especially promising as, in comparison to the simple multiplicative Gaussian noise model,  
Figure 5: Illustration of synthetic images with speckle noise added by different methods. (**a**,**c**) are two clean images. (**b**) is a noisy image of (**a**), with multiplicative Gaussian noise (with \(\delta_{s}=0.3\)) added, and (**d**) is a noisy image of (**c**) with speckle noise added using the Field II toolbox [27; 28].  
the Field II toolbox has the ability of simulating realistic ultrasound images of human tissue [27; 28]. This may enable our method to have a higher chance of better despeckling real ultrasound images in clinical practice.  
We also used normal bilateral filtering followed by our compensation strategy, and no clear improvement was found over the normal bilateral filtering itself in terms of the PSNR and SSIM metrics. A possible reason is that bilateral filtering breaks the local structures, which are difficult to recover with our compensation strategy.