A piece-wise spatial invariant model of ultrasonic image formation

A model of ultrasonic image formation has been developed for an electronically focused linear-array transducer. An analytical expression for the point-spread function of the image degradation process is obtained. It consists of two terms: one accounts for the electromechanical properties of the transducer; the other describes the diffraction phenomena associated with the wave propagation. To reduce the computational complexity in image restoration, a piecewise-invariant form for the point-spread function has been suggested. Experimental results prove the validity of the model and the feasibility of the reconstruction process with a few shift-invariant filters.