Noise removal and edge detection in ultrasound images by the topological gradient method
Hamdi Houichet, Maher Moakher, Badreddine Rjaibi · New Trends in Mathematical Science · 2019
This paper presents a new approach for the restoration and edge detection in ultrasound images corrupted with Rayleigh-distributed multiplicative noise (speckle).We consider a semilinear PDE from which we derive the asymptotic expansion of the associated Dirichlet energy functional.We give a theoretical expansion of the topological sensitivity approach to detect and preserve the edge set in the ultrasound image during the restoration process.For the numerical solution, we design a fully-discrete forward Euler-Galerkin stepping algorithm and we present some results which illustrate the efficiency of the proposed approach.