2.2.4 | Heursure
Heuisure is a threshold selecting method that combines both sqtwolog and rigrsure methods. If the SNR is small, the rigrsure method’s estimation is poor. In that case, the fixed-form threshold from sqtwolog is used, and vice versa.
2.3 | Proposed gradient-based adaptive wavelet de-noising (gaWD) method
The above traditional wavelet threshold selection methods perform not so well in PA signal de-noising. Based on the characteristics of acquired PA signal, in this work, we propose a new gradient-based adaptive wavelet de-noising (gaWD) method. We first decompose the signal into 6 layers, using wavelet daubechies 8 (db8), shown in FIGURE 1 (a). After careful evaluation, we find that D1, D2, and D3 layers are mainly noise layers. The coefficients with large magnitude among these three layers are not the target PA signal’s main components. In the opponent, they are mainly from the large coupled signal at the transducer surface. The other coefficients in D1, D2 and D3 layers are usually much smaller than D4, D5, and D6 layers. D4, D5 and D6 layers are composed of both noise and signal components, where the magnitude of noise components is much lower than target PA signal. From D4 to D6, the wavelet coefficients go gradually closer to low frequency range, which means that the coefficients in D6 is more important than D4 and D5. What’s more, the magnitude of wavelet coefficients represents signal energy, which means that from perspective of energy, we can get a threshold T from a more important layer D6, then apply it to D4 and D5, the two less important layers, ensuring filtering out all the coefficients with lower energy than target signal of D6 layer. Following this strategy, we sort D6 from smallest to largest, and name the new wavelet coefficients as D6_sort. After that, find the second largest gradient drop in D6_sort, which separates the target signal from the noise components. Then we set the corresponding coefficient value as threshold T. The whole threshold selection process is shown in FIGURE 1 (b). After selecting the threshold, we further use hard thresholding method. For D1, D2, D3 layers, we set them all to zero. For D4, D5, D6 layers, we set all the coefficients below the threshold T to zero and preserve all the coefficients above the threshold T. The whole coefficients selection process is shown in FIGURE 1 (c).