We propose an image representation scheme combining the local and nonlocal characterization of patches in an image. Our representation scheme can be shown to be equivalent to a tight frame constructed from convolving local bases (e.g. wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g. spectral basis induced by nonlinear dimension reduction on patches), and we call the r...

Conventional wisdom in signal processing heavily relies on the concept of inner product defined in the Hilbert space. Despite the popularity of Hilbert-space formulation, we argue it is overly-structured to account for the complexity of signals arising from the real-world. Inspired by the works on fractal image decoding and nonlocal image processing, we propose to view an image as the fixed-poi...

Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such...

Blocking artifact, characterized by visually noticeable changes in pixel values along block boundaries, is a common problem in block-based image/video compression, especially at low bitrate coding. Various post-processing techniques have been proposed to reduce blocking artifacts, but they usually introduce excessive blurring or ringing effects. This paper proposes a self-learning-based post-pr...

Segmentation and classification are prolific research topics in the image processing community, which have been more and more used in the context of analysis of cementitious materials, on images acquired with Scanning Electron Microscopes (SEM) . Indeed, there is a need to be able to detect and to quantify the materials present in a cement paste in order to follow the chemical reactions occurri...

We propose an image denoising method that exploits both nonlocal image modeling and locally adaptive anisotropic estimation. The method uses grouping of adaptive-shape neighborhoods whose surrounding square supersets have been found similar by a blockmatching procedure. The data deÞned on these grouped neighborhoods is stacked together, resulting in 3-D data structures which are generalized cyl...

Most state-of-the-art video-denoising algorithms assume an additive noise model, but such a model does not often reflect true conditions experienced in practice. In this paper, two main issues are addressed, namely, segmentation-based block matching and estimation of noise level. Unlike previously reported block-matching methods, the present method uses an efficient algorithm to perform block m...

Non-local means (NLM) is a popular image denoising scheme for reducing additive Gaussian noise. It uses a patch-based approach to find similar regions within a search neighborhood and estimate the denoised pixel based on the weighted average of all the pixels in the neighborhood. All the pixels are considered for averaging, irrespective of the value of their weights. This thesis proposes an imp...

The need for image restoration is encountered in many practical applications. For instance, distortion due to Additive White Gaussian Noise (AWGN) or in some cases the multiplicative (speckle) one can be caused by poor quality image acquisition. Wavelet denoising attempts to remove these types of noise present in the signal while preserving the signal characteristics, regardless of its frequenc...

In this paper we propose a generic recursive algorithm for improving image denoising methods. Given the initial denoised image, we suggest repeating the following ”SOS” procedure: (i) (S)trengthen the signal by adding the previous denoised image to the degraded input image, (ii) (O)perate the denoising method on the strengthened image, and (iii) (S)ubtract the previous denoised image from the r...