Study on An Accurate Diffraction Tomography Reconstruction Algorithm Based on Compressive Sensing

To overcome the problem of low accuracy of the traditional diffraction ultrasound tomography reconstruction algorithm, an accurate ultrasonic diffraction tomography reconstruction algorithm based on compressive sensing is proposed in this paper. Firstly, the kernel matrix of generic simple and efficient Fast Fourier Transforms (GFFT), non-uniform fast Fourier transforms (NUFFT) using Min-Max Interpolation (Min-Max-NUFFT) and Least Square non-uniform fast Fourier transforms (LS-NUFFT) are used to interpolate the non- Cartesian projection data of k space into the Cartesian grid respectively. Secondly, the optimization problem of compressed sensing is constituted by the uniform distribution of the projected data and the total variable difference of the reconstructed image. Finally, the iterative image reconstruction is fulfilled with a gradient descent method. Simulations results show that the reconstruction accuracy of the proposed algorithm is higher than that of the NUFFT method, and the artifact in the image is also largely suppressed.