Research On Compressed Sensing Super Resolution Imaging Algorithm With Image Self-restoration

Compressed sensing as the emerging data sampling theory, on the condition that asignal is compressible or sparse in a transform domain, it can reconstruct thehigh-dimensional signal from a small amount of low-dimensional measurements with highprobability. The sparsity has a great effect in the reconstructed image quality. Apply thecompressed sensing in image reconstruction, it has the substantially the same comparedwith image super-resolution reconstruction. Therefore, the idea of image super resolutionreconstruction based on compressed sensing is worth studying. This paper aroundmultiscale geometric analysis method of image sparse theory and image super resolutionreconstruction based on compressed sensing to develop, algorithm，the specific workinclude:Based on harmonic analysis for image representation，we expand the research aroundthe image multiscale geometric analysis method, in view of the existing methods can nottake into account the image transform with low redundancy and anti-frequency aliasingwhen directional filtering, we design a low redundant image multiscale transform based ona new anti-aliasing direction filtering, The transform, directly in the discrete domain，iscombined with two filter banks..First we use the wavelet transform for image multiscaledecomposition, To enhance the direction sensitivity of the basis function, we construct adirectional filter bank with compactly supported in the frequency domain, we conduct tofilter the directions for high frequency wavelet coefficients without aliasing. The spectrumoutside filtered directional subband is set to0, we use this feature to construct novel"Folding" strategy for removing redundancy. It is efficient for reducing redundancy andthe decimated directional subbands with shift invariance avoid the aliasing, whichimproves the direction selectivity of directional filter bank. The simulation results showthat, in sparse representation, denoising and other fields, the the novel image multiscaletransform achieves good results.Considering that there is a deviation between the measurement image and the realimage because of the measurement system physical characteristics restrictions and measurement environmental impact. In order to achieve image transfer, repair, and superresolution imaging without increasing the system complexity, a new compressed sensingsystem is designed based on the theory of compressed sensing and image degeneratemodel. This system modifies the measurement matrix by using the down-samplingoperator and blurring operator of the image degenerate model as well as employ the lowredundant image multiscale transform based on a new anti-aliasing direction filtering，thencombine with the iterative hard threshold algorithm to reconstruct images. The noise limitis regarded as the iteration stopping criteria, which can remove the measurement noise,and a Poisson-singular-integral operator is introduced for deblurring as well assuppressing the amplification of the noise. Experimental results demonstrate theeffectiveness of our system in the quality of the reconstructed images and computingefficiency.For the lack of the existing compressed sensing based super resolution reconstruction,we establish a minimum set of valid measurement based compressed sensing algorithm. Inorder to reduce measurement redundancy, we construct local adaptive sparse dictionariesin wavelet domain to achieve a better sparse representation. And we remove the crosscorrelation coefficients of measurement matrix and dictionaries as possible according tothe mutual coherence theory, we establish the minimum set of valid measurements in thepremise of ensuring signal reconstruction. We use the split augmented lagrangianshrinkage threshold algorithm to reconstruct images by employing the variables of spatialand frequency domain as constraints for each other alternately. The proposed compressedsensing algorithm, restrained by the constructed the minimum set of valid measurements,can reconstruct high-resolution, high-quality images with richly detailed by using themeasurements which is much less than those of traditional compressed sensing.