Lower bound on image filtering mean squared error in the presence of spatially correlated noise
Mikhail Uss, Oleksii S. Rubel, Владимир Васильевич Лукин, Benoît Vozel, Kacem Chehdi · 2014
This paper addresses a model-based approach to determine a lower bound on image filtering mean squared error (MSE). Noise is assumed additive and spatially correlated. One particular image class is considered: stochastic isotropic texture with fractal structure. The derived lower bound on filtering MSE, MSEfBm, is studied as a function of texture roughness, noise variance, and spatial correlation. Simulations show that for practically interesting window size of 15 by 15 pixels MSEfBmcould be reached by the corresponding ML estimator. The derived bound is used to assess the efficiency of well-known DCT based filter (the version adapted to spatially correlated noise). Situations where DCT-filter is the most and the least effective are identified.