FIGURE 4 The SNR of de-noised signal after proposed gaWD method, low pass filtering, sqtwolog threshold, minimaxi threshold, hersure threshold, and rigrsure threshold method, from left to right, respectively.
gaWD method achieves a much cleaner signal with higher SNR.
FIGURE 4 shows the calculated SNR of the 6 different de-noising methods mentioned above. Our proposed gaWD method exhibits the highest SNR, about 3 dB above the low pass method, and much higher than the others.
4 | PA IMAGING SIMULATION RESULTS
In order to further verify our proposed algorithm, we use the k-wave toolbox in MATLAB to perform PA simulation study. Sixty-four acoustic sensor elements are set in a circle to receive PA signals generated from a segment of blood vessel. Since the sensors’ distribution is sparse, the image will be blurred if we directly reconstruct the image. Here we first interpolate the recorded data on a continuous measurement surface before image reconstruction. The original distribution of both the vessel and sensors are shown in FIGURE 5(a). The reconstructed initial pressure distribution using interpolated data, without adding any noise, is shown in FIGURE 5(b). Then, we add 18dB noise to the raw PA data, leading to a noisy PA image in FIGURE 5(c). We perform 4-order Butterworth filtering, sqtwolog WTD, and our proposed method. The imaging results are shown in FIGURE 5(d), (e), (f), respectively. We can easily find that 4-order Butterworth filter blurs the vessel along with limited de-noising performance. The sqtwolog WTD de-noising method reduce much noise, but it also causes severe vessel signal distortion. In comparison, our proposed method achieves better de-noising performance without obvious signal distortion.
To be more quantitative, the PSNR and SSIM of these images are calculated according to the following equations (5)-(8)15-17.
\begin{equation} \mathbf{\text{\ \ \ \ \ \ \ \ }}\text{\ \ }MSE\ =\ \frac{1}{\text{mn}}\sum_{i=0}^{m-1}{\sum_{j=0}^{n-1}{{||f(i,j)-g(i,j)||}^{2}\text{\ \ \ \ \ \ \ \ \ \ }(5)}}\nonumber \\ \end{equation}\begin{equation} \ \ \ \ \ \ \ PSNR\ =\ 10\log_{10}\left(\frac{\text{MAX}_{I}^{2}}{\text{MSE}}\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (6)\nonumber \\ \end{equation}\begin{equation} \text{SSIM}\left(f,g\right)=\ l\left(f,g\right)c\left(f,g\right)s\left(f,g\right)\ \text{\ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ (7)\nonumber \\ \end{equation}\begin{equation} \left\{\begin{matrix}\text{\ l}\left(f,g\right)=\ \frac{2\mu_{f}\mu_{g}+C_{1}}{\mu_{f}^{2}+\mu_{g}^{2}+C_{1}}\text{\ \ \ }\\ \ c(f,g)\ =\ \frac{2\sigma_{f}+\sigma_{g}+C_{2}}{\sigma_{f}^{2}+\sigma_{g}^{2}+C_{2}}\\ s\left(f,g\right)=\ \frac{\sigma_{\text{fg}}+C_{3}}{\sigma_{f}\sigma_{g}+C_{3}}\text{\ \ \ \ \ \ \ }\\ \end{matrix}\right.\ \mathbf{\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }}\ (8)\nonumber \\ \end{equation}