Abstract
Abstract The Lorentzian norm of robust statistics is often applied in the reconstruction of the sparse signal from a compressed measurement signal in an impulsive noise environment. The optimization of the robust statistic function is iterative and usually requires complex parameter adjustments. In this article, 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. The proposed method requires neither complex optimization nor complex parameter adjustments. The performance of the proposed method was evaluated on 60 images. The experimental results indicated that the proposed method effectively rejected the impulsive noise. Furthermore, at the same impulsive noise corruption level, the reconstruction with the proposed method as the preprocessing required much lower measurement rate than the model-based Lorentzian iterative hard thresholding.
Highlights
Compressed sensing (CS) is a sampling paradigm that provides compressible signals at a rate significantly below the Nyquist rate
It iteratively applies the heuristic rule that is based on the energy distribution of the image data in wavelet domain to detect the existence of the impulsive noise
The values in the table indicated that the proposed method was unable to keep the percentage of inaccurate rejection to less than 1% if the magnitude of the impulsive noise was less than 2.5 ymax
Summary
Compressed sensing (CS) is a sampling paradigm that provides compressible signals at a rate significantly below the Nyquist rate. In [15], the reconstruction from the signal corrupted by the impulsive noise is performed by solving one of the following two optimization problems. Where eδ and a are a sparse vector with large non-zero coefficients (impulsive noise) and a pre-defined threshold, respectively; ||u||TV is a total variation norm of u. This method first estimates s and estimates eδ. It iteratively applies the heuristic rule that is based on the energy distribution of the image data in wavelet domain to detect the existence of the impulsive noise. The proposed method detects the impulsive noise via the energy distribution of the projected sparse signal.
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