Robust image reconstruction algorithm in the presence of gaussian and impulsive noise for compressed sensing

Abstract

The Compressed Sensing (CS) reconstruction methods robust to Gaussian and/or impulsive noise are proposed in this dissertation. In the first part, the reconstruction in the Gaussian noise environment is proposed. The compressed measurement signal is subsampled for L times to create the ensemble of L compressed measurement signals. Orthogonal Matching Pursuit with Partially Known Support (OMP-PKS) is applied to each signal in the ensemble to reconstruct L noisy outputs. The L noisy outputs are then averaged for Gaussian denoising. The proposed method was evaluated on 40 test images and found to improve both PSNR and visual quality of the reconstructed results. In the second part of this dissertation, the reconstruction in the impulsive noise environment is investigated. In conventional methods, the impulsive noise tolerance is acquired by using the Lorentzian norm of robust statistics. The optimization of the robust statistic function is iterative and usually requires complex parameter adjustments. In this part, the impulsive noise rejection for the compressed measurement signal with the design for image reconstruction is proposed. It is used as the preprocessing for any compressed sensing reconstruction given that the sparsified version of the signal is obtained by utilizing octave-tree discrete wavelet transform with db8 as the mother wavelet. The presence of impulsive noise is detected from the energy distribution of the reconstructed sparse signal. After the noise removal, the noise corrupted coefficients are estimated. Moreover, the proposed method requires neither complex optimization nor complex parameter adjustments.In addition, the two proposed methods can be combined to create the reconstruction robust to both Gaussian and impulsive noise.