Compressed sensing and sparsity in photoacoustic tomography

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 backprojection. 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.

A sparsification and reconstruction strategy for compressed sensing photoacoustic tomography

“…In this work we develop a new framework for CS PAT that allows to bring sparsity into play. Our approach is rooted in the concept of sparsifying temporal transforms developed for PAT in [30,20] for two and three spatial dimensions. However, the approach in this present paper extends and simplifies this transform approach considerably.…”

“…On the other hand, most works on discrete settings consider both discrete spatial and time variables [22,19]. The above setting (2) has been considered in a few works [30,20,10]. It well reflects the high sampling rate of the time variable in many practical PAT systems.…”

Deep Learning Versus <tex>$\ell^{1}$</tex> -Minimization for Compressed Sensing Photoacoustic Tomography

“…with m ( M. Several choices for the measurement matrix S are possible and have been used for CS PAT [2][3][4]. In this work, we take S as deterministic sparse subsampling matrix or Bernoulli random matrix; see Subsection 5.1.…”

“…Compressed sensing (CS) allows to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. A reduced number of measurements can increase the measurement speed and reduce system costs [1][2][3][4][5] . However, CS PAT image reconstruction requires special algorithms to achive high resolution imaging.…”

Special issue on optoacoustic imaging and sensing

“…They include a highly sensitive magneto-motive photoacoustic and ultrasound imaging method [2], a new parallel acoustic delay line array for real-time photoacoustic tomography [3], a gas-coupled laser acoustic detection method for both photoacoustic and ultrasound imaging [4], a forward-viewing photoacoustic imaging probe for endoscopic diagnosis [5]. Compressed sensing and sparsity in photoacoustic tomography is investigated in [6]. There are also two papers on life-time photoacoustic imaging [7,8].…”