Microwave induced thermoacoustic tomography based on probabilistic reconstruction

The performance of the existing reconstruction algorithms based on compressive sensing (CS) in microwave induced thermoacoustic tomography (MITAT) is influenced by the positions of detectors. Besides, some a priori information, such as target distribution or the correlation among thermoacoustic signals, has not been taken into account. In this letter, a probabilistic reconstruction algorithm in MITAT based on sparse Bayesian learning is proposed. Different from norm-based point estimation algorithms in CS, the sound pressure distribution which needs to be estimated is provided by probability distributions in the probabilistic reconstruction algorithm and an image is reconstructed based on the posterior density. Compared with the widely used norm-based point estimation algorithms (GPSR, Lasso) whose solution is not always the sparsest, the sparse Bayesian learning framework is globally convergent which can produce the sparsest solution at the posterior mean. Therefore, the robustness of the probabilistic reconstruction is better than that of norm-based point estimation algorithms. In addition, the estimations of the initial pressure distributions can be more accurately provided if the correlation of thermoacoustic signals can be considered, especially under the condition of low signal to noise ratio (SNR). Simulations and experiments on real breast tumors demonstrate that the proposed algorithm improves the robustness of reconstruction and show better performance at low SNRs.