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We propose a method for altering pixel statistics of one image according to another (source) image. Given an input or observed image (probably degraded by one or more unknown processes), and a source image exhibiting the general patch (group of pixels) properties expected in the input image (before degradation), we seek to infer the original image and the process that affected it to produce the observed image. The foundation of our approach is to transform known image patches with desired statistics to patches found in the input image using a finite set of filters or transformations. These transformations are unknown; thus they also must be estimated. We cast this problem as an approximate probabilistic inference problem and show how it can be approached using belief propagation and expectation maximization. Experimental results for joint image restoration and filter estimation are presented.