Reconstruction using optimal spatially variant kernel for B-mode ultrasound imaging

We propose a technique that allows the improvement of lateral resolution in ultrasound imaging using a deconvolution-based strategy. We first derive a formulation for the problem in terms of an arbitrary spatially-variant beam pattern and show that it is possible to optimally estimate the values of the image by solving a large linear inverse problem. This linear system depends on the shape and extent of the point spread function as well as the desired resolution of the resultant image. We show that this linear system is sparse and therefore sparse matrix techniques for storage and algebra are used to make the computational cost reasonable. The strategies used to solve this problem are proposed based on truncated singular value decomposition or regularized conjugate gradient method that allows an equivalent regularization to imposing a quadratic inequality constraint. This allows the condition number of the problem to be kept sufficiently low, thus ensuring a robust solution. For a given ultrasound line with specific transmit and receive focusing characteristics, this problem is solved for the whole image and we show that it is possible to implement the solution in a look-up table form similar to what is used in image reconstruction in current ultrasound systems. This accounts for the variations of the point spread function at different spatial positions.