Block based compressive sensing method of microwave induced thermoacoustic tomography for breast tumor detection

Microwave induced thermoacoustic tomography (MITAT) is a developing non-ionized technique which has great potential in early breast tumor detection. In our previous work, an imaging method, CS-MITAT, was proposed, which applied the compressive sensing theory in MITAT and achieved a good image. The method converts a signal model into an unconstrained optimization problem with ℓ1 norm regularization, which only exploits the spatial sparsity of targets. In this paper, based on the block sparsity of thermoacoustic signals and target distribution in MITAT, the signals to be detected can be grouped into several blocks and the summation of ℓ2 norm regularization is used to replace the ℓ1 norm regularization of the CS-MITAT method. The combination of ℓ2 and ℓ1 norm regularizations helps the aggregation of nonzero elements which are accumulated in blocks. A priori structural constraint is added to form a more realistic signal model which can improve the image quality. Compared with the conventional approach of time reversal mirror and the method of gradient projection for sparse reconstruction, the alternating direction method of multipliers is applied to solve the convex optimization problem. Simulations and experiments on a real breast tumor demonstrate the effectiveness of the proposed method.