Measurement matrix uncertainty model-based microwave induced thermoacoustic sparse reconstruction in acoustically heterogeneous media

Microwave induced thermoacoustic has attracted broad attention in recent years because of its potential for clinical noninvasive detection. The model matrix in the model-based reconstruction method is often constructed by simulation, assuming that the media is acoustically homogeneous. However, the thermoacoustic signal waves propagate through acoustically heterogeneous media in real imaging scenes and are recorded by sparse sensor array. Thus, there is a perturbation between the actual and pre-designed measurement matrix, called measurement matrix uncertainty. In this Letter, an improved model is proposed to reconstruct the sound pressure distribution from sparse signals with phase distortion caused by variations in the speed of sound between tissues. The measured thermoacoustic signals are employed to construct a series of complex signals, which contain amplitude and phase information. The signal model's sparse constraint of the estimated sound pressure map is combined with the nonzero constraint of the random measurements' phases with respect to the amplitude-only measures. Our simulation and experiment results indicate that the proposed model helps to improve the image quality reconstructed by sparse sampling in acoustically heterogeneous media.