Efficient regularization with wavelet sparsity constraints in photoacoustic tomography
In this paper, we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we derive a wavelet-vaguelette decomposition (WVD) for the PA...
Saved in:
Published in | Inverse problems Vol. 34; no. 2; pp. 24006 - 24033 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
IOP Publishing
01.02.2018
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | In this paper, we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we derive a wavelet-vaguelette decomposition (WVD) for the PAT forward operator and a corresponding explicit reconstruction formula in the case of exact data. In the case of noisy data, we combine the WVD reconstruction formula with soft-thresholding, which yields a spatially adaptive estimation method. We demonstrate that our method is statistically optimal for white random noise if the unknown function is assumed to lie in any Besov-ball. We present generalizations of this approach and, in particular, we discuss the combination of PAT-vaguelette soft-thresholding with a total variation (TV) prior. We also provide an efficient implementation of the PAT-vaguelette transform that leads to fast image reconstruction algorithms supported by numerical results. |
---|---|
Bibliography: | IP-101325.R1 |
ISSN: | 0266-5611 1361-6420 |
DOI: | 10.1088/1361-6420/aaa0ac |