Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a computationally intensive process of image restoration. Specifically, each patch has to undergo a patch classification step and a shrinkage step. These two steps can be efficiently solved with a GMM prior but are computationally impractical when using a GGMM prior. In this paper, we provide approximations and computational recipes for fast evaluation of these two steps, so that EPLL can embed a GGMM prior on an image with more than tens of thousands of patches. Our main contribution is to analyze the accuracy of our approximations based on thorough theoretical analysis. Our evaluations indicate that the GGMM prior is consistently a better fit for modeling image patch distribution and performs better on average in image denoising task.
Traditional metrics for evaluating the efficacy of image processing techniques do not lend themselves to understanding the capabilities and limitations of modern image processing methods -particularly those enabled by deep learning. When applying image processing in engineering solutions, a scientist or engineer has a need to justify their design decisions with clear metrics. By applying blind/referenceless image spatial quality (BRISQUE), Structural SIMilarity (SSIM) index scores, and Peak signal-to-noise ratio (PSNR) to images before and after image processing, we can quantify quality improvements in a meaningful way and determine the lowest recoverable image quality for a given method.
Image restoration methods aim to recover the underlying clean image from corrupted observations. The expected patch log-likelihood (EPLL) algorithm is a powerful image restoration method that uses a Gaussian mixture model (GMM) prior on the patches of natural images. Although it is very effective for restoring images, its high runtime complexity makes the EPLL ill-suited for most practical applications. In this paper, we propose three approximations to the original EPLL algorithm. The resulting algorithm, which we call the fast-EPLL (FEPLL), attains a dramatic speed-up of two orders of magnitude over EPLL while incurring a negligible drop in the restored image quality (less than 0.5 dB). We demonstrate the efficacy and versatility of our algorithm on a number of inverse problems, such as denoising, deblurring, super-resolution, inpainting, and devignetting. To the best of our knowledge, the FEPLL is the first algorithm that can competitively restore a pixel image in under 0.5 s for all the degradations mentioned earlier without specialized code optimizations, such as CPU parallelization or GPU implementation.
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