Study On Underdetermined Image Blind Source Separation Based On Sparse Component Analysis

Blind source separation is a kind of powerful signal processing technology developped inrecent years. Image blind source separation is one of the important branches. It is a process ofrestoring the source images with the mixed images under the circumstances of unknowing anypriori knowledge of the source images and the mixed way. It can solve the problem ofdegradation of images, such as stains and noise, when images are to obtain, use and save.Independent component analysis is a classic algorithm of blind source separation. But thesource signals need to satisfy the Gaussian distribution and statistically independent to each otherwhen using it. And it also doesn’t apply to underdetermined blind source separation. In this case,sparse component analysis algorithm appears. It overcomes the drawback of independentcomponent analysis. The source signals can be accurately separated just needing that they aresparse or can be sparse represented. Sparse component analysis includes two basic methods: theadaptive method and the two-phase method. The paper mainly studies using the latter one toseparate source images.Sparse representation of images is the premise of using sparse component analysisalgorithm for blind source separation. Therefore the paper firstly introduces the image sparserepresentation theory. The design of sparse dictionary is mainly introduced. It is divided intoanalysis dictionary and learning dictionary. The MATLAB simulation results verify theperformance of the two kinds of dictionary.Then, the first stage of the two-phase method that how to estimate the mixed matrix is fullystudied. The paper puts forward two new algorithms: improved k-means (fuzzy c-means)clustering algorithm and improved linear clustering algorithm. The MATLAB simulation resultsshow that improved algorithms can better estimate the mixed matrix with shorter time than theformer ones.Lastly, the paper introduces the second stage of the two-phase method. It is the problem ofhow to restore the source images. Underdetermined blind source separation model is convertedinto compression perception model. We can restore the source images with reconstructionalgorithms of compression perception when the mixed matrix is known. Three reconstructionalgorithms are introduced in detail. They are respectively orthogonal matching pursuit algorithm,basis pursuit algorithm and smoothingl0algorithm. For the fixed complete dictionary has thedisadvantages that the separation accuracy is not high, a cyclic iterative method to trainover-complete dictionary is put forward. For image signals have large amount of calculation, wecan divide images into blocks. The MATLAB simulation results verify the advantages of sparse component analysis and the improved algorithm. It is also proved from accuracy and time thatsmoothingl0algorithm is the most suitable reconstruction algorithm to restore the sourceimages.