Compressed sensing and sparsity in photoacoustic tomography

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 apply 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 for reducing the number of spatial measurements without reducing the spatial resolution.ope

Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

Practical applications of thermoacoustic tomography require numerical inversion of the spherical mean Radon transform with the centers of integration spheres occupying an open surface. Solution of this problem is needed (both in 2-D and 3-D) because frequently the region of interest cannot be completely surrounded by the detectors, as it happens, for example, in breast imaging. We present an efficient numerical algorithm for solving this problem in 2-D (similar methods are applicable in the 3-D case). Our method is based on the numerical approximation of plane waves by certain single layer potentials related to the acquisition geometry. After the densities of these potentials have been precomputed, each subsequent image reconstruction has the complexity of the regular filtration backprojection algorithm for the classical Radon transform. The peformance of the method is demonstrated in several numerical examples: one can see that the algorithm produces very accurate reconstructions if the data are accurate and sufficiently well sampled, on the other hand, it is sufficiently stable with respect to noise in the data

Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double layer potentials for the wave equation, for the domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.Comment: 9 figure

A practical guide to photoacoustic tomography in the life sciences

The life sciences can benefit greatly from imaging technologies that connect microscopic discoveries with macroscopic observations. One technology uniquely positioned to provide such benefits is photoacoustic tomography (PAT), a sensitive modality for imaging optical absorption contrast over a range of spatial scales at high speed. In PAT, endogenous contrast reveals a tissue's anatomical, functional, metabolic, and histologic properties, and exogenous contrast provides molecular and cellular specificity. The spatial scale of PAT covers organelles, cells, tissues, organs, and small animals. Consequently, PAT is complementary to other imaging modalities in contrast mechanism, penetration, spatial resolution, and temporal resolution. We review the fundamentals of PAT and provide practical guidelines for matching PAT systems with research needs. We also summarize the most promising biomedical applications of PAT, discuss related challenges, and envision PAT's potential to lead to further breakthroughs