Local adaptive processing in sliding transform domains for image restoration and noise removal with preservation of edges and detail boundaries represents a substantial advance in the development of signal and image processing techniques, thanks to its robustness to signal imperfections and local adaptivity (context sensitivity). Local filters in the domain of orthogonal transforms at each position of a moving window modify the orthogonal transform coefficients of a signal to obtain only an estimate of the central pixel of the window. A minimum mean-square error estimator in the domain of sliding discrete cosine and sine transforms for noise removal and restoration is derived. This estimator is based on fast inverse sliding transforms. To provide image processing at a high rate, fast recursive algorithm for computing the sliding sinusoidal transforms are utilized. The algorithms are based on a recursive relationship between three subsequent local spectra. Computer simulation results using synthetic and real images are provided and discussed. © 2010 Copyright SPIE - The International Society for Optical Engineering.