Fast Signal Sparse Decomposition Based On GAMP And Atom Dictionary Creation With Gaussian Kernel

Instead of calculating inner product between residual and all the atoms in sparsedecomposition, Matching Pursuit algorithm based on Genetic optimization applies a randomsearch to capture an approximate optimal atom in each iteration fast and efficiently. Gaussiankernel function has the smallest time-frequency window area, concerning that a structureadaptive redundant dictionary can be constructed. Besides, a pseudo atom with merely centralregion retained can be employed to approach signals than the whole atom due to itsexponential decay characteristic and symmetrical waveform. This thesis focuses on a fast andefficient sparse decomposition and dictionary for image representation. Main contributionsare as follows:1. According to the process of cross, mutation, big mutation and the scale variability,where (n-1)/4individuals are crossed instead of mutation, the big mutation has a lineardecreasing upper limit, and a mutation applied to random stable selected subset rather than theentire individuals. Besides, a linear decreasing contains Metropolis criterion is added to scale,which improves the accuracy and accelerates the decomposition.2. Searching precision and evolutionary t is compared with variable genetic generations.When the generation is40, GAMP algorithm ensures the evolution precision and avoids a tsurge in decomposition.3. To avoid duplicate compute inner product between the same atom and residuals, asame atomic product substitution method is involved, where the same atomic product value isstored in decomposition.4. Mathematical properties of basic generating function derives from Gaussian kernel isanalyzed. Due to the hard threshold discrimination criterion, a Central Region can beextracted, and devices a relation between the one-dimensional Gabor atoms central region anddiscrete parameters, where the energy ratio between central region and the entire atomexceeds95%.5. The properties of anisotropic2D Gabor over-complete dictionary and Gaussiankernel edge dictionary are studied. By applying discrete translation, scaling, rotation andcosine modulation to Gaussian kernel function, a Gaussian kernel structure dictionary is constructed, which can matching the smooth, roof edge, step edge and texture structure ofimage properly, and the range of discrete parameters are proposed. Meanwhile, the FFT isapplied to MP, so that the smooth, edge and texture sub-dictionary can match the imagefeatures adaptively and fast.