Deconvolution based photoacoustic reconstruction with sparsity regularization

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.