An envelope signal based deconvolution algorithm for ultrasound imaging

To improve the quality of medical ultrasound images, a number of restoration methods based on demodulated signals have been proposed in the literature. However, due to the shift of center frequency of transmitted ultrasound pulses at different penetration depth in a lossy medium, it is hard to determine the exact center frequency at a specified position so to achieve satisfactory demodulation. In this paper, this problem is dealt with by a novel restoration method based on envelope models of the radio frequency (RF) and the point spread function (PSF) signals. To cope with the ill inverse problem caused by the narrow band PSF, an envelop signal based sparse regularized deconvolution model is derived under a sparsity assumption of the tissue reflectivity function (TRF). Furthermore, a two-step iterative shrinkage/thresholding (TwIST) method based alternating minimization approach is applied to compute the optimal solution of the proposed deconvolution problem. Finally, the robustness and the practicability of the proposed method are demonstrated by a series of experiments on both numerical simulation and in vivo data. The experimental results show that the proposed method can achieve significant improvement of the ultrasound images in terms of the resolution gain and signal-to-noise ratio (SNR).