Log In Sign Up

Compressed sensing photoacoustic tomography reduces to compressed sensing for undersampled Fourier measurements

by   Giovanni S. Alberti, et al.

Photoacoustic tomography (PAT) is an emerging imaging modality that aims at measuring the high-contrast optical properties of tissues by means of high-resolution ultrasonic measurements. The interaction between these two types of waves is based on the thermoacoustic effect. In recent years, many works have investigated the applicability of compressed sensing to PAT, in order to reduce measuring times while maintaining a high reconstruction quality. However, in most cases, theoretical guarantees are missing. In this work, we show that in many measurement setups of practical interest, compressed sensing PAT reduces to compressed sensing for undersampled Fourier measurements. This is achieved by applying known reconstruction formulae in the case of the free-space model for wave propagation, and by applying the theories of Riesz bases and nonuniform Fourier series in the case of the bounded domain model. Extensive numerical simulations illustrate and validate the approach.


page 21

page 23

page 25

page 26

page 27

page 28


Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing

A signature result in compressed sensing is that Gaussian random samplin...

Dynamic Compressed Sensing for Real-Time Tomographic Reconstruction

Electron tomography has achieved higher resolution and quality at reduce...

Multi-Scale Factorization of the Wave Equation with Application to Compressed Sensing Photoacoustic Tomography

By performing a large number of spatial measurements, high spatial resol...

Removing Stripes, Scratches, and Curtaining with Non-Recoverable Compressed Sensing

Highly-directional image artifacts such as ion mill curtaining, mechanic...

Joint Compressed Sensing and Manipulation of Wireless Emissions with Intelligent Surfaces

Programmable, intelligent surfaces can manipulate electromagnetic waves ...

Derandomizing compressed sensing with combinatorial design

Compressed sensing is the art of reconstructing structured n-dimensional...

Recovering quantum gates from few average gate fidelities

Characterising quantum processes is a key task in and constitutes a chal...