Robust Recursive Inverse Adaptive Algorithm in Impulsive Noise

Abstract

The recently proposed Recursive Inverse (RI) algorithm has shown a significant performance improvement compared to that of the Recursive Least Squares (RLS) algorithm, in various noise environments. However, both algorithms fail to converge in certain impulsive noise environments, especially if the Signal-to-Noise Ratio (SNR) is low. In this paper, a Robust RI algorithm is proposed. Analytical results show that robustness against impulsive noise is achieved by choosing the weights on the basis of the L 1 norms of the autocorrelation matrix and the crosscorrelation vector. Simulation results confirm that the proposed algorithm provides an improved performance, with a reduction in computational complexity, compared to those of the RLS and the Robust RLS in white and correlated impulsive noise.

Reconstruction of Sparse Signals in Impulsive Disturbance Environments

“…Then, a direct application of the recovery algorithm on the remaining samples is possible, [32] (or in image processing [24]). This kind of approach can be used, in general, when a knowledge about the disturbance behavior can help us to detect the positions of the corrupted samples [1,8,11,20,21,37].…”

“…Signals having a sparse B Ljubiša Stanković ljubisa@ac.me 1 University of Montenegro, 81000 Podgorica, Montenegro representation can be reconstructed from a reduced subset of randomly positioned samples. Processing of these signals with a large number of missing/unavailable samples attracted significant interest in the recent years within the theory of compressive sensing (CS) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]22,30,31,33,34,36].…”

“…In contrast to the methods that combine the robust estimation and the CS-based signal recovery, here we assume that we cannot distinguish the corrupted samples from the uncorrupted ones based on their values. This assumption, along with signal sparsity assumption, makes this approach different from the common robust filtering techniques [1,8,11,20,21,35,37]. Furthermore, the proposed approach can provide reconstruction with a user-defined precision, rather than to obtain its filtered approximation.…”

Efficient Restoration Method for Images Corrupted with Impulse Noise

“…To overcome this problem, many algorithms, mainly modified forms of median filters, have been proposed [2-9, 11-19, 21-23]. Different approaches have also been addressed, such as those proposed in [1,20].…”

“…In [1], a robust recursive inverse algorithm is proposed to restore images which are mainly corrupted by impulsive noise with low signal-to-noise ratio.…”