## 4 Experimental Results and Discussion
### Clinical Liver Ultrasound Images
Figure 7b shows the results for the proposed method using Dictionary 1 (PSNR = 30.3345 dB) and Figure 7c shows the results for the proposed method using Dictionary 2 (PSNR = 30.8073). It is clear that the image denoised using the proposed SR method reconstructed image very close to the original image. It can also be seen that the dictionary trained on the noisy image gives better results than using a set of multiple references images. The results of this comparative experiment show that the proposed algorithm not only reduces the speckle noise but also preserves the edge information. Table 2 shows the PSNR and MSSIM values to quantify the results numerically for noise parameter \(\sigma=15\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **PSNR (dB)** & **MSSIM** \\ \hline [PERSON] & 28.966 & 0.822 \\ Median & 25.497 & 0.659 \\ [PERSON] & 27.772 & 0.782 \\ SRAD & 28.766 & 0.813 \\ [PERSON] & 28.279 & 0.801 \\ [PERSON] & 29.218 & 0.834 \\ Proposed: Dictionary 1 & 30.334 & 0.901 \\ Proposed: Dictionary 2 & 30.807 & 0.926 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PSNR and MSSIM for the ultrasound liver image for \(\sigma=15\). Figure 6: Reconstruction of liver right lobe images. (**a**) Original ultrasound image; (**b**) Speckled ultrasound image (PSNR = 28.148 dB); Images reconstructed using (**c**) Dictionary 1 (PSNR = 35.033 dB) and (**d**) Dictionary 2 (PSNR = 35.537 dB). Speckle is an arbitrary granular texture noise that degrades ultrasound image quality. This experiment was performed to evaluate different noise variances by comparing the PSNR obtained using the proposed algorithm and other despeckling algorithms. The simulated result using the noise levels 10, 15, 20, 25, and 30 are illustrated in Figure 8. The results clearly depict that, for different noise variances, the proposed algorithm gives the best PSNR value of all the algorithms on speckle reduction. Figure 7: Despeckled results obtained for the ultrasound liver dataset using a linear transducer with a frequency of 8 MHz. The red and the green boxes highlight the differences observed from the noisy and filtered images. (**a**) Speckled image and results yielded by the proposed method using (**b**) Dictionary 1 and (**c**) Dictionary 2 as well as results using the (**d**) Frost; (**e**) median; (**f**) Kuan; (**g**) wavelet; (**h**) Weiner; and (**i**) SRAD filters. The experiments presented above were performed on ultrasound liver images, and the performance compared with conventional methods. However, our algorithm can also be utilized for a wide range of ultrasound images. To prove this, we conducted experiments on a real thrombus (blood clot) image with a left ventricular mass [56]. The visual assessment was performed using the proposed technique and the results compared to those obtained by various other algorithms. The reference image size was 256 \(\times\) 256 pixels in order to fit our proposed model. The data were obtained from an open medical imaging dataset on GitHub [57]. The ultrasound image along with a marked note are shown in Figure 9a. The dashed white box in Figure 9b-j indicate regions of the ventricular mass. The thrombus data-set results presented in Figure 9h-j show that the wavelet, Weiner, and SRAD filters performed very poorly in noise reduction. The difference can be seen from the white note marked on the right atrium of the reference ultrasound image in Figure 9a. Figure 9e-g shows that Frost, median, and Kuan reduces speckle but tends to over-smooth the image, which leads to the loss of a distinctive feature of the unclear mass. Among all the methods, Figure 9c,d show good results for the SR-based on learned dictionaries 1 and 2. Several details are well preserved and the speckle noise is reduced efficiently. Figure 10 shows the zoomed sub-images of Figure 9 to observe a clear visualization of the despeckled images. The red box highlights the texture details in the noisy image and the filtered image for a comparative visual assessment.