This work extends the Bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems. We address the restoration of images with poor spatial correlation as well as strongly correlated (natural) images. The spatial nonlinearity employed in the final estimation step of the Bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images. For spatially correlated images, the nonlinearity design is rather conducted using a particular wavelet decomposition that, detecting lines, edges, and higher order structures, carries out a task analogous to those of the (preattentive) stage of the human visual system. Experimental results pertaining to restoration of motion blurred text images, out-of-focus spiky images, and blurred natural images are reported.
A twin stage texture synthesis-by-analysis method is presented. It aims to approximate first- and second-order distributions of the texture, accordingly to the Julesz conjecture. In the first stage, the binary textural behavior of a given prototype is represented by means of a hard-limited Gaussian process. In the second stage, the texture is synthesized by passing the binary hard-limited Gaussian process through a linear filter followed by a zero memory histogram equalizer.
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