A Study Of Sparse Coding Algorithms And Their Applications

The sparse coding (also referred to as sparse neuro-representation) of natural images studied in this dissertation is an artificial neural network (ANN) method, which can model the receptive fields of simple cells in the mammalian primary visual cortex in brain, also known as V1. This method has the capacity of simulating all characteristics of the receptive fields of simple cell neurons, i.e., spatially localized, oriented, and bandpass (selective to the structure at different spatial scales). More over, the encoding realization for this method only depends on the statistical properties of natural perceptive information, regardless of the inherent properties of input data. Therefore, sparse coding is a self-adaptive signal statistical method.Nowadays, sparse coding (SC) technique has been applied in speech signal separation, visual image processing, biologic DNA miroarray data classification and pattern recognition, etc. However, generally neurophysiologists know a little about V1 at present, so the sparse coding technique is still at a developing stage, and the investigation of theory and application should be enhanced and improved further.In this dissertation, after a brief introduction to the biologic background of the primate visual system, the development history, the current research status and shortcomings of SC, a simple mathematic description to SC was given also. Then, some algorithms and applications of SC were investigated at large, and many more efficient methods and further improvements to the current existing methods were presented. The main works in this dissertation can be introduced as follows:1. A modified SC model simulating the respective fields of simple cells in the main visual cortex V1 is proposed in this dissertation. The classical SC algorithm has the following disadvantages: (1) The convergent speed is very slow; (2) It can not simultaneously guarantee the sparsity and independence of coefficient components; (3) The objective function itself can not balance between the sparseness constraint and the reconstructed precision. To remove or avoid the disadvantages mentioned above, referred to as the classical SC algorithm, we propose a novel SC algorithm, which exploits the maximum Kurtosis as the maximizing sparse measure criterion, so the natural image structure captured by the Kurtosis is not only sparse, and is but also surely independent. At the same time, a fixed variance term of coefficients is used to...