Lower bound on image filtering mean squared error in the presence of spatially correlated noise

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, MSE_fBm, 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 MSE_fBm could 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.