Reconstrução de imagens de ultrassom usando esparsidade: métodos iterativos rápidos

Abstract

This study contributes to the search for fast iterative methods for ultrasonic sparse image reconstruction. The goal is achieved in three steps: the validation of a discrete acquisition model, a comparative evaluation of algorithms suitable to the problem and an acceleration proposal for one of the best performing methods. The model validation strategy consists of image reconstructions from synthetic data with previously known results, and subsequent validation with real data, collected by an ultrasound research platform with a professional phantom. The reconstructions are performed by a selected set of iterative algorithms of convex optimization, which have their parameters, results and performances analyzed. This study proposes the acceleration of the ADMM (Alternating Direction Method of Multipliers), which is among the best performing methods in terms of computational cost, and which can have its initial convergence speed doubled by the proposed modification. Since the acceleration can also be used in other applications of ADMM, the proposed modification is validated in four cases of study: two in ultrasonography and two in magnetic resonance imaging.