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We consider the problem of recovering an unknown signal observed through a nonlinear model and corrupted with additive noise. More precisely, the nonlinear degradation consists of a convolution followed by a nonlinear rational transform. As a prior information, the original signal is assumed to be sparse. We tackle the problem by minimizing a least-squares fit criterion penalized by a Geman-McClure...
Mammography is still the most effective procedure for early diagnosis of the breast cancer. Computer-aided Diagnosis (CAD) systems can be very helpful in this direction for radiologists to recognize abnormal and normal regions of interest in digital mammograms faster than traditional screening program. In this work, we propose a new method for breast cancer identification of all types of lesions in...
Recent work in video compression has shown that using multiple 2D transforms instead of a single transform in order to de-correlate residuals provides better compression efficiency. These transforms are tested competitively inside a video encoder and the optimal transform is selected based on the Rate Distortion Optimization (RDO) cost. However, one needs to encode a syntax to indicate the chosen...
In this paper we propose a dictionary learning method that builds an over complete dictionary that is computationally efficient to manipulate, i.e., sparse approximation algorithms have sub-quadratic computationally complexity. To achieve this we consider two factors (both to be learned from data) in order to design the dictionary: an orthonormal component made up of a fixed number of fast fundamental...
Recent developments in the standardisation of High Efficiency Video Coding (HEVC) have shown that the block-wise activation/deactivation of a colour transform can significantly improve the compression performance. This coding tool is based on a fixed colour space which is either YCgCo in lossy compression mode or YCgCo-R in the lossless mode. The proposed method shows that the performance can be increased...
Compressed sensing is a signal acquisition scheme that measures signals at sub-Nyquist rate amenable to sparse recovery, with high probability, from a reduced set of measurements. One of the main requirements of compressive sensing is the sparsity of the class of signals of interest in some basis. A method to construct a sparsifying basis for a class of signals using information theoretic measures...
Multiple transforms have received considerable attention recently, especially in the course of an exploration conducted by MPEG and ITU toward the standardization of the next generation video compression algorithm. This joint team has developed a software, called the Joint Exploration Model (JEM) which outperforms by over 25% the HEVC standard. The transform step in JEM consists in Adaptive Multiple...
In this paper we examine the general problem of estimating the frequency of a balanced or unbalanced three-phase power system. The Clarke transform is commonly employed to transform the three real voltages to in-phase and quadrature components that are combined to form a complex exponential, the frequency of which can then be estimated. The imbalance between the voltages in an unbalanced system results...
Block matching 3D collaborative filtering (BM3D) is one of the most popular denoising technique based on data sparsity concept applied to specially structured data. In this paper we develop this technique for complex domain, i.e. for application to complex-valued data. Sparsity as an approximation technique can be addressed directly to complex-valued variables or to real-valued pairs phase/amplitude...
In this paper, we develop a robust generalization of the Gaussian quasi score test (GQST) for composite binary hypothesis testing. The proposed test, called measure-transformed GQST (MT-GQST), is based on a transformation applied to the probability distribution of the data. The considered transform is structured by a non-negative function, called MT-function, that weights the data points. By appropriate...
The goal of pattern matching is to find small parts of an image that are similar to a given template. Matching in transform-domain (such as Haar, Walsh-Hadamard, etc.) is more efficient that matching in the spatial domain. However, it has a limitation: the template size is restricted to be a power of two to apply fast computational algorithms of transforms. In this paper, fast pattern matching method...
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