ИСТИНА

The article is concerned with developing effective methods for solving inverse problems of ultrasonic tomography. The mathematical model employed describes the effects of ultrasound diffraction, refraction, multiple scattering and absorption. The problem of tomographic image reconstruction is posed as a coefficient inverse problem for the wave equation. The objective is to find the global minimum of the residual functional between the wave field measured at the detectors and the wave field computed for some approximate acoustic parameters of the inspected object. The residual functional may have local minima. To solve such problems, multistage iterative gradient-based method (MSM) is proposed. Low-frequency sounding signals are used at the first stages of the multistage method, ensuring the convergence of approximate solutions obtained at each stage to the exact solution of the inverse problem. The proposed method is demonstrated on model problems of breast ultrasound tomographic imaging for early-stage cancer diagnosis. The iterative method is computationally expensive. Computational efficiency of the proposed method on multi-core CPU and GPU computing platforms is discussed.