Total Variation Algorithms for PAT Image Reconstruction

Medical imaging is an essential part of disease diagnosis, which makes use of technologies such as X-ray, Magnetic Resonance Imaging (MRI), Ultrasound scan, and many more. X-rays are ionizing radiation and cannot be used for frequent examinations, whereas MRI is non-ionizing, but it is costly and time-consuming. Ultrasound scan is frequently used in scanning and is noninvasive but suffers from the problem of low image quality, which can lead to incorrect diagnoses. The efficiency of these methods depends on how invasive, fast, and accurate the imaging method is. Recently, a new method called Photoacoustic Tomography (PAT) is gaining attention due to its ability to produce images with high resolution and high contrast in long penetration depths. A system matrix could be developed from the pseudospectral matrix by evaluating it on different time samples for different sensor locations. Compressive Sensing (CS) algorithms can thus be developed using the system matrix obtained, and their performance could be evaluated. CS is based on how sparse the reconstruction could be. This is mainly based on the regularizer used along with the prior information. In this paper, we propose split Bregman formulation of isotropic and anisotropic total variation with
$l_{1}$
and
$l_{2}$
regularization for efficient PAT image reconstruction. The proposed methods have better reconstruction efficiency in terms of computation time and image quality while maintaining the sparsity. When evaluating the various TV formulations for PAT image reconstruction, it is observed that anisotropic
$\text{TV}-l_{2}$
is the most efficient one, generating superior image quality and accomplishing the reconstruction in less than 1 second, enabling quick medical imaging and early diagnosis.