Deconvolution based photoacoustic reconstruction with sparsity regularization

Abstract

In most photoacoustic tomography (PAT) reconstruction approaches, it is assumed that the receiving transducers have omnidirectional response and can fully surround the region of interest. These assumptions are not satisfied in practice. To deal with these limitations, we present a novel deconvolution based photoacoustic reconstruction with sparsity regularization (DPARS) technique. The DPARS algorithm is a semi-analytical reconstruction approach in which the projections of the absorber distribution derived from a deconvolution-based method are computed and used to generate a large linear system of equations. In these projections, computed over limited viewing angles, the directivity effect of the transducer is taken into account. The distribution of absorbers is computed using a sparse representation of absorber coefficients obtained from the discrete cosine transform. This sparse representation helps improve the numerical conditioning of the system of equations and reduces the computation time of the deconvolution-based approach by one order of magnitude relative to Tikhonov regularization. The algorithm has been tested in simulations, and using two-dimensional and three-dimensional experimental data obtained with a conventional ultrasound transducer. The results show that DPARS, when evaluated using contrast-to-noise ratio and root-mean-square errors, outperforms the conventional delay-and-sum (DAS) reconstruction method.

Sparsity-based photoacoustic image reconstruction with a linear array transducer and direct measurement of the forward model

“…A deconvolution-based PA reconstruction was invented with sparsity regularization in a three-transducer PAT system. 21 The algorithm is a semianalytical approach, where the sparsity regularization improves the numerical conditioning of the system of equations and reduces the computation time of the deconvolution-based process. A full-wave iterative image reconstruction was developed based on TV regularization in PAT system with acoustically inhomogeneous media.…”

Investigation of photoacoustic tomography reconstruction with a limited view from linear array

“…For example, for a typical ROI of , for the transducer element in the center, the angle is estimated to be 0.24 radians, where the sensitivity only slightly drops to 95% ( ) for our transducer. 22 The maximum angle occurs for the end element and is estimated to be 0.72 radians, where the sensitivity drops to 40% ( ). 22 By comparing the reconstructed images with and without directivity pattern, the effect of the directivity pattern was found to be not significant in our current study.…”

“… 22 The maximum angle occurs for the end element and is estimated to be 0.72 radians, where the sensitivity drops to 40% ( ). 22 By comparing the reconstructed images with and without directivity pattern, the effect of the directivity pattern was found to be not significant in our current study. The forward projection model can be further improved in the future by considering other factors such as the attenuation of light and the limited bandwidth of the transducer.…”

Integrating photoacoustic tomography into a multimodal automated breast ultrasound scanner

“…35 More sophisticated reconstruction algorithms take into account the fact that the measured pressure data are not exactly equal to the actual pressure incident on the detector due to factors such as the electromechanical and spatial impulse responses (SIRs) of the detector. 35,36 We can generalize the measured pressure data as…”

“…It is known, however, that accounting for the SIR is computationally difficult. 35,36 In an attempt to strike a balance, we separate the SIR into a spatial portion that describes the directional sensitivity and a temporal portion that describes the averaging effect due to the finite size of the transducer element E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 8 6 Sðr D ; r; tÞ ¼ S 0 ðr D ; rÞS 1 ðtÞ;…”