Research Of Sparse Representation And Its Application

Signal representation is the basic problem in signal processing.Efficient representation of signal contents lies at the foundation of signal processing tasks.Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description.That is the ability of sparse representation.We can use the sparse representation of signal instead of original signal to reduce costs of signal processing,thus,we can improve the efficiency of signal processing.Sparse representation of signals is presented in twentieth century at the beginning of the nineteen's,which is a new signal representation method.As part of basic research of signal,it can use for handling various tasks such as denoising,restoration,separation,interpolation and extrapolation,compression,sampling,analysis and synthesis,detection,recognition,and more.This sparse model is intriguing and fascinating because of the beauty of its theoretical foundations,the superior performance it leads to in various applications,its universality and flexibility in serving various data sources,and its unified view,which makes all the above signal processing tasks clear and simple.This paper researched the basic technology of sparse signal representation,For an optimization problem with anL₁ norm objective function subject to anL₂ norm inequality constraint,this study shows that there is an approximately linear relationship between theL₁ norm objective functional values and theL₂ norm specifications.This relationship is verified through the use of random and real world industrial data.The obtained results can be employed for?i?estimating theL₁ norm objective functional value without solving the optimization problem numerically;?ii?providing an insight for defining theL₂ norm specification in which a simple method is proposed in this study;and?iii?testing whether the obtained solutions are the globally optimal solutions or not.These advantages are demonstrated via the use of random data.Secondly,this thesis describes a sparse representation based approach to learn a classifier for assessing the video quality without a reference.First we calculate the natural scene statistics?NSS?based spatial features of each frame/image and then learn a dictionary by K-SVD algorithm from NSS features of correct frames.In this work weidentified the fact that correct frame can be represented precisely in terms of dictionary atoms but while representing a distorted frame,the error drastically increases with increase in distortion thus we can easily classify the frames as correct and distorted based on error score calculated by sparse representation framework.This framework has been validated on two datasets and we observe improved accuracies as compared to state-of-art algorithms.