An iterative mixed norm image restoration algorithm

In this paper, we propose an iterative mixed norm image restoration algorithm. A functional which combines the least mean squares (LMS) and the least mean fourth (LMF) functionals is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed approach.

Iterative techniques for restoring colour images are presented. These iterative algorithms have been developed for the restoration of monochromatic images. The colour images are modeled as three spatially related monochromatic images or channels. The interchannel correlation is incorporated into the iterative restoration algorithms in an indirect and in a direct way. Experimental results with simulated and real photographically blurred images are presented. Based on experiments the authors conclude that the incorporation of the interchannel correlation into the algorithms does not necessarily improve the quality of the restored images over the algorithms that ignore the interchannel correlation, but they result in considerable computation savings.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Recently, in the world wide the use of power electronics devices increases sharply. As a result, harmonic pollution becomes a vital problem than before. Harmonics rotate in the power system network and interfere with the system equipments, disturbing their normal operation which can deteriorate the quality of the delivered power. Therefore, efficient method with low computational time is a critical tool to estimate and quantify the harmonic that can be used in online control and mitigation of harmonics. Least Mean Square (LMS) is simple and popular algorithm that has been applied in many applications, but, noise can affect its performance. This paper presents and compare the performance of Least Mean Square (LMS), Least Mean Fourth (LMF) and a combined (LMS/LMF) in estimation harmonic component for the signal corrupted with noise contain low signal to noise ratio (SNR). The results show that LMF and LMS/LMF have better steady state performance as compared to LMS.

In this paper, we present a regularized mixed norm multichannel image restoration algorithm. The problem of multichannel restoration using both within- and between-channel deterministic information is considered. For each channel a functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. We introduce a mixed norm parameter that controls the relative contribution between the LMS and the LMF, and a regularization parameter that defines the degree of smoothness of the solution, both updated at each iteration according to the noise characteristics of each channel. The novelty of the proposed algorithm is that no knowledge of the noise distribution for each channel is required, and the parameters mentioned above are adjusted based on the partially restored image.

Mesh of pyramids and pyramid of meshes implementations of an iterative image-restoration algorithm are proposed. These implementations are based on a single-step regularized iterative restoration algorithm. Both architectures are described as a composition of a mesh and a pyramid. They are compared in terms of area of the VLSI chip and its computation time. >

Mesh and mesh-of-pyramids implementations of iterative image restoration algorithms are proposed. These implementations are based on a single-step algorithm as well as on a multistep iterative algorithm derived from the single step regularized iterative restoration algorithm. One processor is assigned to each picture element, with local memory depending on the support of the restoration filter. The implementations consist of interprocessor communication and intraprocessor computations. The efficiency of the proposed VLSI algorithms is judged by establishing lower bounds on AT/sup 2/, where A is the area of the VLSI and T is its computation time. >

Least-Mean Square algorithm, or simply the LMS, is generally one of the most commonly used techniques for optimized solution in adaptive schemes especially in the Gaussian environment. However, least mean fourth (LMF) algorithm and its variants, such as normalized LMF (NLMF), perform better in the non-Gaussian environment. The conventional LMF algorithms usually diverge in non-Gaussian environment with dynamic input. Conventionally, regularization is archived by using a small constant compensation term in the denominator of the learning rate to protect the algorithm from divergence. This paper introduces an efficient time-varying regularized normalized least mean fourth (R-NLMF) algorithm. In the proposed algorithm, the regularization term is made time varying and gradient adaptive according to steepest descent approach. Thus the proposed algorithm adapts its learning rate according to the environment and the input signal dynamics. A similar approach, namely Generalized Normalized Gradient Descent (GNGD) algorithm, has been previously applied to the normalized least mean-square (NLMS) algorithm in the Gaussian environment. However, due to its dependence on NLMS, the GNGD algorithm performance degrades in non-Gaussian environment. In order to overcome this problem, an efficient regularized NLMF algorithm for non-Gaussian environment is proposed. The algorithm shows promising results and achieves faster convergence while maintaining lesser steady-state miss-adjustment. Simulations are carried out to support the theoretical development.

In this work, the convergence analysis of the variable weight mixed-norm least-mean squares (LMS)-least mean-fourth (LMF) adaptive algorithm is derived. The proposed algorithm minimizes an objective function defined as a weighted sum of the LMS and LMF cost functions, where the weighting factor is time varying and adapts itself to allow the algorithm to keep track of the variations in the environment. As a by-product of this novel approach, new necessary and sufficient conditions for the LMF algorithm have been derived. Furthermore, a more general expression for the excess steady-state error for the LMF algorithm has been derived.

We present an iterative adaptive hybrid image restoration algorithm for fast convergence. The local variance, mean, and maximum values are used to constrain the solution space. These parameters are computed at each iteration step using a partially restored image at each iteration, and they are used to impose the degree of local smoothness on the solution. The resulting iterative algorithm exhibits increased convergence speed and better performance than typical regularized constrained least-squares approach.

This paper introduces different types of nonstationary constrained iterative image restoration algorithms. The adaptivity of the algorithm is introduced by the constraint operator which incorporates properties of the response of the human visual system. The properties of the visual system are represented by noise masking and visibility functions. A new way of computing the masking function is also introduced. The proposed algorithms are general and can be used for any type of linear constraint and distortion operators. The algorithms can also be used to restore signals different than images, since the constraint operator can be interpreted as adapting to the local signal activity.

In this paper, we propose a new mixed norm LMS-LMF adaptive algorithm. The algorithm minimizes an objective function defined as a weighted sum of the least mean fourth (LMF) and least mean square (LMS) cost functions. The weighting factor is time varying and adapts itself so as to emphasize one cost function over the other based on proximity to the optimum. Improved convergence is illustrated by examples. Bounds on the step size to ensure mean convergence are also derived.

An adaptive filtering algorithm that minimizes the variance on the squared error subject to a constraint on the mean-squared error (MSE) is proposed. For the adaptive-linear-combiner signal-processing configuration, this algorithm, called the LVCMS algorithm (for least variance subject to a constraint on mean squared error) has a gradient that is a weighted linear combination of the least-mean-square (LMS) and least-mean-fourth (LMF) algorithm gradients. Theoretical expressions are derived for the LVCMS algorithm convergence factor and misadjustment, and comparisons are made with the LMS and LMF adaptive rules for Gaussian, Laplacian, and uniform plant noise nd driving term distributions. Performance comparisons of the LVCMS, LMS, and LMF algorithms based on Monte Carlo simulation studies indicate that the LVCMS adaptation rule not only can yield a small variance of the squared error but it also produces favorable values of the mean-squared error and the mean-squared coefficient error. >

Adaptive equalization is undoubtedly one of the cornerstones of digital communication as it allows for fast and reliable data transmission over practical channels that are non-ideal and that are plagued with serious problems such as signal dispersion and non-Gaussian interferences. In such cases, the performance of the well-known least-mean square (LMS) algorithm or that of any of its variants remains sub-optimal at best. As a remedy to this, the least-mean fourth (LMF) algorithm was later proposed but its high computational load was found to be a constraining factor in its practical implementation, particularly for real-time applications. Inspired from a previous work done on the LMS [1], we recently proposed a new algorithm [2], termed LMF-PTQ, combining the power of the LMF with the implementational advantages of the power-of-two quantization scheme. In this work, we demonstrate, through an extensive simulation study, the effectiveness of our proposed LMF-PTQ algorithm in the equalization of a time-varying channel in a CDMA system which suffers from both signal dispersion and non-Gaussian disturbances. The results obtained so far are very encouraging and provide us with ample enthusiasm to investigate the proposed algorithm further.

In this paper, we show that a class of iterative signal restoration algorithms, which includes as a special case the discrete Gerchberg-Papoulis algorithm, can always be implemented directly (i.e. non-iteratively). In the exactly- and over-determined cases, the iterative algorithm always converges to a unique least squares solution. In the under-determined case, it is shown that the iterative algorithm always converges to the sum of a unique minimum norm solution and a term dependent on initial conditions. For the purposes of early termination, it is shown that the output of the iterative algorithm at the rth iteration can be computed directly using a singular value decomposition-based algorithm. The computational requirements of various iterative and non-iterative implementations are discussed, and the effect of the relaxation parameter on the regularization capability of the iterative algorithm is investigated.

This paper presents a robust generalized modified Blake-Zisserman adaptive filter (GMBZAF)-based control scheme for a three-phase grid-tied single-stage photovoltaic system (GTPVS) to improve power quality (PQ). The GMBZAF-based control scheme enables GTPVS to integrate maximum PV power into the grid with power quality (PQ) improvement at the grid side, such as maintaining balanced sinusoidal grid currents, current harmonics mitigation, reactive power assistance to the inductive load at steady-state, and even during dynamic conditions (variable load and irradiance). The GMBZAF is implemented to accurately calculate the active and reactive weight components of load current. The GTPVS is modeled using MATLAB/Simulink, and its response is observed at steady-state, unbalanced loading, and variable solar irradiance conditions. The comparative assessment between the proposed control scheme and the existing adaptive filtering-based control schemes such as least mean square (LMS) and least mean fourth (LMF) is done.