k-space based regularization of a new pulse-echo image reconstruction operator

A novel regularization approach for reconstructive ultrasound pulse-echo imaging is introduced. This approach is based on weighted minimum-norm least-squares (WMNLS) solution derived from a discretized model of wave propagation in the region of interest (ROI). In previous work, regularization based on model rank reduction or single-parameter WMNLS was used. Even though provided initial proof of concept, these approaches lacked physical intuition and often resulted in artifacts in the point spread function (psf) that were hard to control. In this paper, we introduce a new WMNLS that explicitly utilizes the k-space frequency components of the coded wavefront in the regularization process. The weighting matrix in the WMNLS is derived based on `desired' k-space representation of the imaging operator. This approach directly controls the lateral and axial frequency characteristics of the imaging operator and, therefore, the spatial and contrast resolution of the overall imaging system.