Research On Image Sparse Representation And Applications

Image processing technology has been become one of very important methods forinformation acquisition in human society, and has been widely used in space technology,medical imaging, remote sensing image processing, industrial control, computer vision,video and multimedia systems, etc. Thus, the study on high efficient image processingsystem has deep significance. Biological visual system has been proved to be veryefficient for image processing. Accompanied by the deep study on brain science, manyresearch results on biological visual system are reported, from the primary propertyextraction to high level perceptual organization. Currently, the perception mechanismand related core technologies of visual system have become a very important researchfield of cognitive science.From the start input stimulated by the scene light on retina, visual system uses acomplete set of information processing mechanism to deal with the input image.Although, we have not understood the whole mechanism of visual system, the sparserepresentation ways for input features are accepted by many researches and proved bymany neurophysiology experiments. An efficient sparse coding method must be withmultiscale, critical sampling, and over-complete properties, and the basis function mustbe with local, directional, and anisotropic properties. Base on these principles, thispaper studied the basic image sparse coding model, multiscale and multiresolutiontheory for image processing, over-complete representation methods for imageprocessing, and visual cortex neuron model (the pulse coupled neural networks). Themain research work and contributions are summarized as follows:1. An image sparse representation algorithm over optimal Gabor dictionary isproposed. For image sparse representation, one of the key factors is to constructan efficient over-complete dictionary.2-D Gabor function has perfect local,directional, and space-frequency selective properties; this is very similar to thereceptive field properties of simple cells in primary visual cortex. The dictionaryelements generated by Gabor function can well match the geometric structure(e.g., edge, texture) in natural image, and can achieve well sparse representationfor image. However, because of the over-complete demands, the elements of thisdictionary are very bulky, and lead to an intensive computational efficiency inorthogonal pursuit matching procedure. To overcome this problem, two mainstrategies are adopted:(1) divide the original image into overlapped patches to reduce the length of input sample;(2) adopt Particle Swarm Optimization (PSO)algorithm to imitate the competition activity of neurons in visual cortex. In theoptimization procedure of PSO, the norm of the projection of input signal on thedictionary element is used as fitness value, to optimize a set of optimal Gaborparameters is used to replace the pursuit procedure on the whole dictionary. At thefinal stage of the algorithm, the Orthogonal Matching Pursuit (OMP) algorithm isused for image coding. Experimental results demonstrate that our algorithm canachieve high reconstructed image quality under a low algorithm complexity.2. The traditional algorithm can not adapt to noise environments in transformdomain. To alleviate this problem and improve the adaptability and the noiserobustness of them, a novel multi-sensor image fusion algorithm based on imagesparse representation theory is introduced. For the new algorithm, the relatedimage is partitioned into image patches, and the patches are decomposed by theOMP algorithm, then the sparse coefficients are selected demanding theirprominent property. The selected coefficients are used for the reconstructed imagepatches, and the patches are realigned according to the partition order. Finally, theoverlapped patches are averaged to get the fused image. Experimental resultsshow that the proposed algorithm is with anti-noise property, and outperforms thetypical algorithms in term of objective criteria and visual appearance.3. These methods based on sample learning are more efficient for imagesuper-resolution (SR). However, there are always one-to-many mappings betweenlow-resolution (LR) image patches and high-resolution (HR) image patches. Toovercome or at least reduce the problem induced by the disagreement of LR andHR patches, an algorithm based on image sparse representation and onlinedictionary leaning method is proposed for single image SR problem. Thealgorithm is processed by two stages:1) Training stage. A set of HR images areused as HR samples. They are blurred, subsampled and then upsampled toconstructed the LR samples which are with same size with the HR samples, thenthese two sample sets are filtered to get the feature sample set. The LR featuresample set is used to obtain LR dictionary and the sparse code by onlinedictionary learning algorithm and OMP algorithm. Because LR samples and HRsamples can share the sparse code, the HR dictionary can be calculated;2)Reconstruction stage. When a LR image is inputted, it is also filtered to constructthe feature sample set, and then be processed by the OMP algorithm to get itssparse code. These codes are shared by the HR dictionary to estimate the HR patches. Finally, all the HR patches are arranged according their partitioning order,and the overlapped patches are averaged to reconstruct the HR image. Theexperimental results show that the proposed algorithm outperforms in bothobjective and subjective evaluation compared with several conventional methods.Moreover, the proposed method performs better for detail and texture recover, andalso can reduce the artifacts around edge in the reconstructed HR image.4. A fast image denoising algorithm based on a modified Nonsubsampled ContourletTransform (NSCT) combined with Gaussian Scale Mixtures Model (GSM) isproposed. The Multiscale Geometric Analysis (MGA) theory can achieve optimalsparse representation for high dimension function and can lead to highperformance over wavelets. As one of the effective tools of MGA, the NSCT iswith fully shift-invariant, multiscale, and multidirection properties. For imagedenoising, the algorithm using NSCT combined with GSM seems to be one of theexcellent options. However, the computational efficiency of it is lower. Aiming atthis problem, a modified NSCT is proposed to be applicable to wide applicationsin speed demanding environments. Since the Nonsubsampled Directional FilterBank (NSDFB) mainly affects the performance of NSCT, an optimizedDirectional Filter Bank (DFB) with lifting scheme is adopted to modify theNSDFB for a fast NSCT. Moreover, combined with GSM, the modified NSCT isused for image denoising. The numerical experiments show that the processingspeed of the proposed algorithm is increased by11times than that of theconventional one, while keeping good visual quality of the denoised image.5. In view of the applied peculiarity of ordinary optics, based on the new LaplacianPyramid (LP) transform and the Pulse Coupled Neural Networks (PCNN), a novelmultifocus image fusion algorithm which is with antinoise properties is proposed.For the algorithm, the new LP transform is adopted to construct the pyramidal dataof the related images; the data is then inputted into PCNN. Through the iterativeoperation by the PCNN, the firing map of neurons can be obtained, and then thesemaps are used by the decision operator for data fusion. The fused pyramidal dataare reconstructed by the new pseudo inverse (also named dual frame operator) toobtain the fused image. The experimental results show that new algorithmoutperforms the traditional algorithm, both in visual appearance and objectiveevaluation criteria. The PSNR value increases19.4percent than that of the old LPalgorithm. Moreover, the proposed algorithm is with antinoise properties foradditive noise and system noise from JPEG compression, and can efficiently reduce the “pseudo Gibbs” phenomenon which is inevitable in the fused image bythe old LP algorithm.