# Biomedical Photoacoustic Imaging Optimization with Deconvolution and EMD Reconstruction
## 3 Results  
### Numerical Simulations  
We implemented numerical simulations based on the MATLAB (The MathWorks, Natick, MA, USA) k-Wave toolbox [20] using a HP server (Hewlett-Packard, Palo Alto, CA, USA), which has 2 Intel (Intel Corporation, Santa Clara, CA, USA) Xeon (R) X5670 CPU working at 2.93 GHz and 72.0 GB RAM. PA data were detected by 128 linear ultrasound element transducers, which distributed on the upper side of the numeric phantom. The speed of sound was set to 1540 m/s. In the simulation, two numeric phantoms were used to validate the effectiveness of our proposed method. To prevent the interference of the reconstruction method in k-Wave toolbox, we used the basic delay-and-sum reconstruction algorithm to reconstruct each image in our study.  
First, the deconvolution kernel \(h(n)\) was acquired from a single transducer element on the upper side, which detects the numeric phantom that only consists of a point source of radius 1 in the middle position. The normalized \(h(n)\), shown in Figure 1a performs as the uniform deconvolution kernel in our simulations.  
To illustrate the deformation of signal and the direct results in reconstructed image clearly, we used a simple numeric phantom as seen in Figure 2a, which consists of a large point source in the middle and four small point sources around. Meanwhile, to make the simulation more realistic, we used a vessel-like image as seen in Figure 3a to simulate the complex numeric phantom.  
Figure 3: Results of the signal processing and reconstruction in complex numeric phantom. (**a**) the set position of source and sensors; (**b**) reconstructed image of original signal; (**c**) reconstructed image of de-convolved signal; (**d**) reconstructed image of final processed signal; (**e**) signal processing result.  
Figure 2: Results of the signal processing and reconstruction in simple numeric phantom. (**a**) the set position of source and sensors; (**b**) reconstructed image of original signal; (**c**) reconstructed image of de-convolved signal; (**d**) reconstructed image of final processed signal; (**e**) signal processing result.  
As observed in Figures 2e and 3e, bipolar N-shape signals are converted to monopolar signals after processing and more detailed information appears, especially in Figure 3e. The small N-shape waves affected by the negative part of the big N-shape waves became apparent. From the reconstructed images in Figures 2 and 3, we can observe that the original signals result in aliasing and blurring in reconstruction (as Figures 2b and 3b), the five dots and the two main branches are hard to distinguish. Moreover, the existence of N-shape wave leads to distortion in the image. Using Figure 2b as an example, the two points in the lower side are obviously weaker than the two points in the upper side, and on the other hand, the position of the two points in the lower side slightly moves downward compared with the set position (Figure 2a). This is because the wave after big waves is affected and even buried by the negative part of the big waves. But by performing deconvolution on signals (Figures 2c and 3c), aliasing is alleviated, and distortion is corrected. After processing by EMD (Figures 2d and 3d), the edge sharpness and resolution of the images were further improved. With the gap widening between main imaging targets, the five dots in Figure 2 and the branches in Figure 3, are distinguishable and separated now.  
Since the original PA signal is bipolar, using an envelope is necessary when reconstructing images by means of delay-and-sum algorithm. However, this step could be left out due to the positive polarity of the refactored signal, which further improves image quality and increases efficiency.