Compressed sensing and sparsity in photoacoustic tomography

TL;DR

This paper introduces a compressed sensing approach for photoacoustic tomography that reduces measurement requirements by using linear measurements and sparsifying transforms, enabling faster imaging without sacrificing resolution.

Contribution

It develops a novel two-stage reconstruction algorithm that leverages sparsity and linear measurements to improve speed and reduce complexity in photoacoustic imaging.

Findings

Significantly fewer measurements needed for high-resolution images

Effective sparsifying transforms for 3D photoacoustic data

Validated on simulated and experimental data

Abstract

Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this issue using techniques of compressed sensing. We demonstrate, that the number of measurements can significantly be reduced by allowing general linear measurements instead of point-wise pressure values. A main requirement in compressed sensing is the sparsity of the unknowns to be recovered. For that purpose we develop the concept of sparsifying temporal transforms for three-dimensional photoacoustic tomography. We establish a two-stage algorithm that recovers the complete pressure Signals in a first step and then applies a standard reconstruction algorithm such as back-projection. This yields a novel reconstruction method with much lower complexity than existing compressed sensing approaches for photoacoustic tomography. Reconstruction results for simulated and for experimental data verify that the proposed compressed sensing scheme allows to significantly reducing the number of spatial measurements without reducing the spatial resolution.