An axially-variant kernel imaging model applied to ultrasound image reconstruction

TL;DR

This paper introduces an axially-variant kernel imaging model for ultrasound image reconstruction that overcomes limitations of traditional models by accounting for spatial variations, leading to improved image quality without increased computational cost.

Contribution

The authors develop a computationally efficient ultrasound imaging model with an axially varying kernel, enabling more accurate deconvolution and image reconstruction.

Findings

Model has same complexity as invariant kernel methods

Simulation confirms model's effectiveness for large images

Reconstruction quality surpasses traditional invariant kernel approaches

Abstract

Existing ultrasound deconvolution approaches unrealistically assume, primarily for computational reasons, that the convolution model relies on a spatially invariant kernel and circulant boundary conditions. We discard both restrictions and introduce an image formation model applicable to ultrasound imaging and deconvolution based on an axially varying kernel, that accounts for arbitrary boundary conditions. Our model has the same computational complexity as the one employing spatially invariant convolution and has negligible memory requirements. To accommodate state-of-the-art deconvolution approaches when applied to a variety of inverse problem formulations, we also provide an equally efficient adjoint expression of our model. Simulation results confirm the tractability of our model for the deconvolution of large images. Moreover, the quality of reconstruction using our model is superior to that obtained using spatially invariant convolution.