Reconstruction of Enhanced Ultrasound Images From Compressed Measurements Using Simultaneous Direction Method of Multipliers

High-resolution ultrasound (US) image reconstruction from a reduced number of measurements is of great interest in US imaging, since it could enhance both frame rate and image resolution. Compressive deconvolution (CD), combining compressed sensing and image deconvolution, represents an interesting possibility to consider this challenging task. The model of CD includes, in addition to the compressive sampling matrix, a 2-D convolution operator carrying the information on the system point spread function. Through this model, the resolution of reconstructed US images from compressed measurements mainly depends on three aspects: the acquisition setup, i.e., the incoherence of the sampling matrix, the image regularization, i.e., the sparsity prior, and the optimization technique. In this paper, we mainly focused on the last two aspects. We proposed a novel simultaneous direction method of multipliers based optimization scheme to invert the linear model, including two regularization terms expressing the sparsity of the RF images in a given basis and the generalized Gaussian statistical assumption on tissue reflectivity functions. The performance of the method is evaluated on both simulated and in vivo data.