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}