Study of L0-norm constraint normalized subband adaptive filtering algorithm

Limited by fixed step-size and sparsity penalty factor, the conventional sparsity-aware normalized subband adaptive filtering (NSAF) type algorithms suffer from trade-off requirements of high filtering accurateness and quicker convergence behavior. To deal with this problem, this paper proposes variable step-size L0-norm constraint NSAF algorithms (VSS-L0-NSAFs) for sparse system identification. We first analyze mean-square-deviation (MSD) statistics behavior of the L0-NSAF algorithm innovatively in according to a novel recursion form and arrive at corresponding expressions for the cases that background noise variance is available and unavailable, where correlation degree of system input is indicated by scaling parameter r. Based on derivations, we develop an effective variable step-size scheme through minimizing the upper bounds of the MSD under some reasonable assumptions and lemma. To realize performance improvement, an effective reset strategy is incorporated into presented algorithms to tackle with non-stationary situations. Finally, numerical simulations corroborate that the proposed algorithms achieve better performance in terms of estimation accurateness and tracking capability in comparison with existing related algorithms in sparse system identification and adaptive echo cancellation circumstances.Comment: 15 pages,15 figure

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme

Robust Total Least Mean M-Estimate normalized subband filter Adaptive Algorithm for impulse noises and noisy inputs

When the input signal is correlated input signals, and the input and output signal is contaminated by Gaussian noise, the total least squares normalized subband adaptive filter (TLS-NSAF) algorithm shows good performance. However, when it is disturbed by impulse noise, the TLS-NSAF algorithm shows the rapidly deteriorating convergence performance. To solve this problem, this paper proposed the robust total minimum mean M-estimator normalized subband filter (TLMM-NSAF) algorithm. In addition, this paper also conducts a detailed theoretical performance analysis of the TLMM-NSAF algorithm and obtains the stable step size range and theoretical steady-state mean squared deviation (MSD) of the algorithm. To further improve the performance of the algorithm, we also propose a new variable step size (VSS) method of the algorithm. Finally, the robustness of our proposed algorithm and the consistency of theoretical and simulated values are verified by computer simulations of system identification and echo cancellation under different noise models

Variable Block Size Motion Compensation In The Redundant Wavelet Domain

Video is one of the most powerful forms of multimedia because of the extensive information it delivers. Video sequences are highly correlated both temporally and spatially, a fact which makes the compression of video possible. Modern video systems employ motion estimation and motion compensation (ME/MC) to de-correlate a video sequence temporally. ME/MC forms a prediction of the current frame using the frames which have been already encoded. Consequently, one needs to transmit the corresponding residual image instead of the original frame, as well as a set of motion vectors which describe the scene motion as observed at the encoder. The redundant wavelet transform (RDWT) provides several advantages over the conventional wavelet transform (DWT). The RDWT overcomes the shift invariant problem in DWT. Moreover, RDWT retains all the phase information of wavelet coefficients and provides multiple prediction possibilities for ME/MC in wavelet domain. The general idea of variable size block motion compensation (VSBMC) technique is to partition a frame in such a way that regions with uniform translational motions are divided into larger blocks while those containing complicated motions into smaller blocks, leading to an adaptive distribution of motion vectors (MV) across the frame. The research proposed new adaptive partitioning schemes and decision criteria in RDWT that utilize more effectively the motion content of a frame in terms of various block sizes. The research also proposed a selective subpixel accuracy algorithm for the motion vector using a multiband approach. The selective subpixel accuracy reduces the computations produced by the conventional subpixel algorithm while maintaining the same accuracy. In addition, the method of overlapped block motion compensation (OBMC) is used to reduce blocking artifacts. Finally, the research extends the applications of the proposed VSBMC to the 3D video sequences. The experimental results obtained here have shown that VSBMC in the RDWT domain can be a powerful tool for video compression