Denoising is the problem of removing noise from an image. The most commonly studied case is with additive white Gaussian noise (AWGN), where the observed noisy image f is related to the underlying true image u by f = u + η, and η is at each point in space independently and identically distributed as a zero-mean Gaussian random variable. Total variation (TV) regularization is a technique that was originally developed for AWGN image denoising by Rudin, Osher, and Fatemi [9]. The TV regularization technique has since been applied to a multitude of other imaging problems, see for example Chan and Shen's book [20]. We focus here on the split Bregman algorithm of Goldstein and Osher [31] for TV-regularized denoising. Source CodeANSI C source code to produce the same results as the demo is accessible on the article web page http://dx.doi.org/10.5201/ipol.2012.g-tvd. Future software releases and updates will be posted at http://dev.ipol.im/~getreuer/code.

While many segmentation methods rely heavily in some way on edge detection, the "Active Contours Without Edges" method by Chan and Vese [7,9] ignores edges completely. Instead, the method optimally fits a two-phase piecewise constant model to the given image. The segmentation boundary is represented implicitly with a level set function, which allows the segmentation to handle topological changes more easily than explicit snake methods. This article describes the level set formulation of the Chan-Vese model and its numerical solution using a semi-implicit gradient descent. We also discuss the Chan-Sandberg-Vese method [8], a straightforward extension of Chan-Vese for vector-valued images.Source Code ANSI C source code to produce the same results as the demo is accessible on the article web page http://dx.doi.org/10.5201/ipol.2012.g-cv. Future software releases and updates will be posted at http://dev.ipol.im/~getreuer/code. Supplementary MaterialA video on the article web page http://dx.doi.org/10.5201/ipol.2012.g-cv shows animated segmentation evolutions for several of the examples in this work.

Robust and far-field speech recognition is critical to enable true hands-free communication. In far-field conditions, signals are attenuated due to distance. To improve robustness to loudness variation, we introduce a novel frontend called perchannel energy normalization (PCEN). The key ingredient of PCEN is the use of an automatic gain control based dynamic compression to replace the widely used static (such as log or root) compression. We evaluate PCEN on the keyword spotting task. On our large rerecorded noisy and far-field eval sets, we show that PCEN significantly improves recognition performance. Furthermore, we model PCEN as neural network layers and optimize high-dimensional PCEN parameters jointly with the keyword spotting acoustic model. The trained PCEN frontend demonstrates significant further improvements without increasing model complexity or inference-time cost.

Given an image where a specified region is unknown, image inpainting or image completion is the problem of inferring the image content in this region. Traditional retouching or inpainting is the practice of restoring aged artwork, where damaged or missing portions are repainted based on the surrounding content to approximate the original appearance. In the context of digital images, inpainting is used to restore regions of an image that are corrupted by noise or where the data is missing. Inpainting is also used to solve disocclusion, to estimate the scene behind an obscuring foreground object. A popular use of digital inpainting is object removal, for example, to remove a trashcan that disrupts a scene of otherwise natural beauty. Inpainting is an interpolation problem, filling the unknown region with a condition to agree with the known image on the boundary. A classical solution for such an interpolation is to solve Laplace's equation. However, Laplace's equation is usually unsatisfactory for images since it is overly smooth. It cannot recover a step edge passing through the region. Total variation (TV) regularization is an effective inpainting technique which is capable of recovering sharp edges under some conditions (these conditions will be explained). The use of TV regularization was originally developed for image denoising by Rudin, Osher, and Fatemi [3] and then applied to inpainting by Chan and Shen [13]. TV-regularized inpainting does not create texture, the method is limited to inpainting the geometric structure. Source CodeANSI C source code to produce the same results as the demo is accessible on the article web page http://dx.doi.org/10.5201/ipol.2012.g-tvi. Future software releases and updates will be posted at http://dev.ipol.im/~getreuer/code.

Automatic Color Enhancement "ACE" is an effective method for color image enhancement introduced by Gatta, Rizzi, and Marini based on modeling several low level mechanisms of the human visual system. The direct computation of ACE on an N × N image costs O(N 4 ) operations. This article describes two fast approximations of ACE. First, the algorithm of Bertalmío, Caselles, Provenzi, and Rizzi uses a polynomial approximation of the slope function to decomposes the main computation into convolutions, reducing the cost to O (N 2 log N ). Second, an algorithm based on interpolating intensity levels also reduces the main computation to convolutions. The use of ACE for image enhancement and color correction is demonstrated. Source CodeANSI C source code to produce the same results as the demo is accessible on the article web page http://dx.doi.org/10.5201/ipol.2012.g-ace.