Non-convex Compressive Sensing Image Reconstruction Method Based On Dictionary Learning

In compressed sensing theory, signal sampling and compression can be performedat the same time while eliminating the process of extracting and discarding data fromredundant data obtained in the high-speed sampling.In this way,the theory can downsampling speed of the sensor and reduce the computational expense.As the keyproblem of the compressed sensing theory,signal reconstruction is al0norm questionessentially,and thel0norm question is an NP-hard problem. In the master’s thesisguidanced by professor Liu Fang and named “Non-convex Comp ressed Sensin gReconstruction Based on Ridgelet Redundant Dictionary”,the author completes imagereconstruction under the learning of Ridgelet redundancy dictionary.The author usemutual-neighbors clustering method to cluster,initial population with single-direction,use genetic algorithm to get the optimal combination of atoms in direction and useclonal selection optimization algorithm to learn a optimal combination of the atomicsin scale and displacement to reconstruct images at last. Experimental results show that,when the sampling rate is30%or higher, the method above can obtain accuracyreconstruction result, but at a lower sampling rate, the result is not satisfactory.In orderto solve this problem, we propose a non-convex compressive sensing imagereconstruction method based on dictionary learning.In this thesis, the main work is asfollows:Since the observation vector can only carry little information at low samplingrate,the results from mutual-neighbors clustering is not satisfactory.In this thesis, withthe local similarity of observation vector and with the difference of standard deviationbetween observation vectors as measurement,we make use of local growth to finish theobservation vector clustering. After clustering the observation vectors, for each class ofthe image blocks,we use improved genetic algorithm to learn the optimal combinationof atoms in direction. After genetic evolution studying,we use clonal selectionoptimization algorithm to learn a optimal combination of the atomics in scale anddisplacement to reconstruct images at last.We have two innovations in geneticalgorithm: Firstly, taking into account the characteristics of both smooth blocks andtexture blocks,for each class of image blocks corresponding to one class of observationvectors,we initialize the populations with both multi-direction andsingle-direction;secondly,we use a kind of local selection mechanism instead of the traditional one to avoid the loss of population diversity.Simulation results show that thetwo innovations can improve the accuracy of the reconstructed image.What’s more,inthe clonal selection optimization algorithm,in order to increase the diversity of thepopulation, the initial population size of this algorithm is not uniform.After conductingpopulation expansion and removing repeated antibodies,we regard the number of theantibodies in current population as population size.The crossover,mutation andselection operations are performed on this scale of the population.In this thesis, we combine genetic evolution algorithm and clonal selectionalgorithm to learn the dictionary in direction, scale and displacement, and use theoptimal combination of the atomics studied from dictionary learning to reconstructimages. Simulation results show that we improve the quality of the reconstructedimage.