Constrained total variation minimization for photoacoustic tomography

Similar to computed tomography, the images from photoacoustic tomography are piecewise smooth and reconstructions can be enhanced by applying Total Variation (TV) minimization. Also, the photoacoustic image must satisfy both the data fidelity and a non negativity constraint. This paper proposes a constrained TV minimization formulation in the Fourier Bessel domain which has the advantage of reducing the dimension of the fidelity constraint and the projection onto this constraint can be performed by a simple projection onto the l₂ ball. The TV minimization post processing improves the quality of images reconstructed and recovers the lost, low frequency information when sensor lower frequency limit is higher than zero.