The Maximum Entropy on the Mean Method for Image Deblurring
This addresses image deblurring for computer vision applications, offering a novel paradigm shift but with incremental improvements in handling noise.
The paper tackles the ill-posed problem of image deblurring by proposing a method that regularizes at the probability distribution level, showing computational feasibility for large blurs and effective kernel approximation with symbology, but it does not actively denoise and requires preconditioning for high noise.
Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. We propose an alternative approach, shifting the paradigm towards regularization at the level of the probability distribution on the space of images. Our method is based upon the idea of maximum entropy on the mean wherein we work at the level of the probability density function of the image whose expectation is our estimate of the ground truth. Using techniques from convex analysis and probability theory, we show that the method is computationally feasible and amenable to very large blurs. Moreover, when images are imbedded with symbology (a known pattern), we show how our method can be applied to approximate the unknown blur kernel with remarkable effects. While our method is stable with respect to small amounts of noise, it does not actively denoise. However, for moderate to large amounts of noise, it performs well by preconditioned denoising with a state of the art method.