A robust M-estimate adaptive equaliser for impulse noise suppression

In this paper, a FIR adaptive equaliser for impulse noise suppression is proposed. It is based on the minimization of an M-estimate objective function which has the ability to ignore or down-weight a large error signal when it exceeds certain thresholds. An advantage of the proposed method is that its solution is governed by a system of linear equations, called the M-estimate normal equation. Therefore, traditional fast algorithms like the recursive least squares algorithm can be applied. Using a robust estimation of the thresholds and the recursive least square algorithm, an M-estimate RLS (M-RLS) algorithm is developed. Simulation results show that the proposed algorithm has better convergence performance than the N-RLS and MN-LMS algorithms when the input signal of the equaliser is corrupted by individually or consecutive impulse noises. It also shares the low steady state error of the traditional RLS algorithm.published_or_final_versio

A Recursive Least M-Estimate Algorithm for Robust Adaptive Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis

This paper studies the problem of robust adaptive filtering in impulsive noise environment using a recursive least M-estimate algorithm (RLM). The RLM algorithm minimizes a robust M-estimator-based cost function instead of the conventional mean square error function (MSE). Previous work has showed that the RLM algorithm offers improved robustness to impulses over conventional recursive least squares (RLS) algorithm. In this paper, the mean and mean square convergence behaviors of the RLM algorithm under the contaminated Gaussian impulsive noise model is analyzed. A lattice structure-based fast RLM algorithm, called the Huber Prior Error Feedback-Least Squares Lattice (H-PEF-LSL) algorithm1 is derived. It has an order O(N) arithmetic complexity, where N is the length of the adaptive filter, and can be viewed as a fast implementation of the RLM algorithm based on the modified Huber M-estimate function and the conventional PEF-LSL adaptive filtering algorithm. Simulation results show that the transversal RLM and the H-PEF-LSL algorithms have better performance than the conventional RLS and other RLS-like robust adaptive algorithms tested when the desired and input signals are corrupted by impulsive noise. Furthermore, the theoretical and simulation results on the convergence behaviors agree very well with each other.published_or_final_versio

A Huber recursive least squares adaptive lattice filter for impulse noise suppression

This paper proposes a new adaptive filtering algorithm called the Huber Prior Error-Feedback Least Squares Lattice (H-PEF-LSL) algorithm for robust adaptive filtering in impulse noise environment. It minimizes a modified Huber M-estimator based cost function, instead of the least squares cost function. In addition, the simple modified Huber M-estimate cost function also allows us to perform the time and order recursive updates in the conventional PEF-LSL algorithm so that the complexity can be significantly reduced to O(M), where M is the length of the adaptive filter. The new algorithm can also be viewed as an efficient implementation of the recursive least M-estimate (RLM) algorithm recently proposed by the authors [1], which has a complexity of O(M 2). Simulation results show that the proposed H-PEF-LSL algorithm is more robust than the conventional PEF-LSL algorithm in suppressing the adverse influence of the impulses at the input and desired signals with small additional computational cost.published_or_final_versio

A robust quasi-newton adaptive filtering algorithm for impulse noise suppression

This paper studies the problem of robust adaptive filtering in impulse noise environment using the Quasi-Newton (QN) adaptive filtering algorithm. An M-estimate based cost function is minimized instead of the commonly used mean square error (MSE) to suppress the adverse effect of the impulse noise on the filter coefficients. In particular, a new robust quasi-Newton (R-QN) algorithm using the self-scaling variable metric (SSV) method for unconstrained optimization is studied in details. Simulation results show that the R-QN algorithm is more robust to impulse noise in the desired signal than the RLS algorithm and other QN algorithm considered. Its initial convergence speed and tracking ability to sudden system change are also superior to those of the quasi-Newton algorithm proposed in [1].published_or_final_versio

Motion picture restoration

This dissertation presents algorithms for restoring some of the major corruptions observed in archived film or video material. The two principal problems of impulsive distortion (Dirt and Sparkle or Blotches) and noise degradation are considered. There is also an algorithm for suppressing the inter-line jitter common in images decoded from noisy video signals. In the case of noise reduction and Blotch removal the thesis considers image sequences to be three dimensional signals involving evolution of features in time and space. This is necessary if any process presented is to show an improvement over standard two-dimensional techniques. It is important to recognize that consideration of image sequences must involve an appreciation of the problems incurred by the motion of objects in the scene. The most obvious implication is that due to motion, useful three dimensional processing does not necessarily proceed in a direction 'orthogonal' to the image frames. Therefore, attention is given to discussing motion estimation as it is used for image sequence processing. Some discussion is given to image sequence models and the 3D Autoregressive model is investigated. A multiresolution BM scheme is used for motion estimation throughout the major part of the thesis. Impulsive noise removal in image processing has been traditionally achieved by the use of median filter structures. A new three dimensional multilevel median structure is presented in this work with the additional use of a detector which limits the distortion caused by the filters . This technique is found to be extremely effective in practice and is an alternative to the traditional global median operation. The new median filter is shown to be superior to those previously presented with respect to the ability to reject the kind of distortion found in practice. A model based technique using the 3D AR model is also developed for detecting and removing Blotches. This technique achieves better fidelity at the expense of heavier computational load. Motion compensated 3D IIR and FIR Wiener filters are investigated with respect to their ability to reject noise in an image sequence. They are compared to several algorithms previously presented which are purely temporal in nature. The filters presented are found to be effective and compare favourably to the other algorithms. The 3D filtering process is superior to the purely temporal process as expected. The algorithm that is presented for suppressing inter-line jitter uses a 2D AR model to estimate and correct the relative displacements between the lines. The output image is much more satisfactory to the observer although in a severe case some drift of image features is to be expected. A suggestion for removing this drift is presented in the conclusions. There are several remaining problems in moving video. In particular, line scratches and picture shake/roll. Line scratches cannot be detected successfully by the detectors presented and so cannot be removed efficiently. Suppressing shake and roll involves compensating the entire frame for motion and there is a need to separate global from local motion. These difficulties provide ample opportunity for further research

Frequency-domain method for measuring alpha factor by self-mixing interferometry

Linewidth enhancement factor, also known as the alpha factor, is a fundamental characteristic parameter of a laser diode (LD). It characterises the broadening of the laser linewidth, the frequency chirp, the injection lock range and the response to external optical feedback. In the past few decades, extensive researches have been dedicated to the measurement of alpha. Among all the existing approaches, the methods based on selfmixing interferometry (SMI) are considered the most simple and effective. The core components of a SMI consist of an LD, a lens and a moving target. When a portion of laser light backscattered or reflected by the external target and re-enters the laser cavity, a modulated lasing field will be generated. The modulated laser power is also called SMI signal, which carries the information of target movement and LD related parameters, including alpha

Least mean M -estimate algorithms for robust adaptive filtering in impulse noise

This paper proposes two gradient-based adaptive algorithms, called the least mean M-estimate and the transform domain least mean M -estimate (TLMM) algorithms, for robust adaptive filtering in impulse noise. A robust M -estimator is used as the objective function to suppress the adverse effects of impulse noise on the filter weights. They have a computational complexity of order O(N) and can be viewed, respectively, as the generalization of the least mean square and the transform-domain least mean square algorithms. A robust method for estimating the required thresholds in the M -estimator is also given. Simulation results show that the TLMM algorithm, in particular, is more robust and effective than other commonly used algorithms in suppressing the adverse effects of the impulses. © 2000 IEEE.published_or_final_versio

Improved Iterative Truncated Arithmetic Mean Filter

This thesis discusses image processing and filtering techniques with emphasis on Mean filter, Median filter, and different versions of the Iterative Truncated Arithmetic Mean (ITM) filter. Specifically, we review in detail the ITM algorithms (ITM1 and ITM2) proposed by Xudong Jiang. Although filtering is capable of reducing noise in an image, it usually also results in smoothening or some other form of distortion of image edges and file details. Therefore, maintaining a proper trade off between noise reduction and edge/detail distortion is key. In this thesis, an improvement over Xudong Jiang’s ITM filters, namely ITM3, has been proposed and tested for different types of noise and for different images. Each of the two original ITM filters performs better than the other under different conditions. Experimental results demonstrate that the proposed filter, ITM3, provides a better trade off than ITM1 and ITM2 in terms of attenuating different types of noise and preserving fine image details and edges