Greedy gap´s Boundary Finder: The impulsive noise rejection for compressed measurement image signal

Impulsive noise in a compressed measurement signal, y, has a significant effect on the reconstruction in Compressed Sensing (CS). In this paper, Greedy gap´s Boundary Finder (GBF), a fast preprocessing for impulsive noise rejection for the CS reconstruction of image signal, is proposed. An image is sparsified by the octave-tree wavelet transform. GBF adopts an idea that the leakage energy out of the third-level (L₃) subband in the reconstructed sparse signal is the result of either the impulsive noise in y or the insufficient information (of y) for reconstruction. The leakage energy is measured as the ratio to the total energy. In a graph of relationship between the energy ratio and the number of the removed elements, there is a gap of low energy ratio in the middle. A binary search is adapted in GBF to find the lower gap´s boundary which is the minimum number of removed elements with low energy ratio. As the image signal is highly redundant, the search in GBF can be non-exact and will be stopped after the number is within +g of the lower boundary, where g is the gap´s resolution and defined as the percent of the size of y. GBF was evaluated on 100 16×16 image blocks and 10 256×256 standard test images. The evaluation shows that at the optimal g of 5%, GBF provided the comparable performance to the exact boundary´s search, but consumed less computational time.