Study On Noise Suppression Theory And Techniques For Signals

Noise suppression for signals is a fundamental and challenging research topic in signal processing field.Benefiting from the promising applications in automatic de-tection,speech recognition,wireless communication,sonar problem,biomedical en-gineering, fiber communication,and so on, oise suppression has become one of the hottest spots in signal processing field in recent years.After more than several decades, the theories and algorithms about noise suppression have great developments.Many effective algorithms have been presented,and their performances are different from de-tection capability, memory requirements,computational cost,etc.However,the noise suppression theory is profound and the related algorithms are difficult to implement. Until nowadays,the study on noise suppression is still far from mature.Many theory problems and noise suppression techniques are expected to continue to be discussed. The main contributions of this thesis are as follows:●Based on sparse modeling technique of signals,we systematically study the basic principle of noise suppression algorithms.The noise suppression problem equals to underdetermined linear system equation solving problem.This problem appears to be difficult in the past,but many examples show that sparse solution of the problem is usually present.The thesis shows how to model the observed signal in a sparse way, demonstrates the theoretical basis for linear system sparse solution, and gives empirical experimental results.The thesis presents:the noisy observed signals can be regarded as the ideal signal and additive noise mixed,which is an underdetermined line system.The only priori knowledge is that noise energy is limited.If we can solve a cost function, the solution containing no more than a certain limit of non-zero solution,i.e.,the error between the estimated solution and the ideal solution is small enough (may good enough to restore the ideal signal).The sparse solution of linear system equations solving problem, can be summarized as two questions to solve:i).Sparse solution existence and necessary conditions for the existence,ⅱ).If a candidate solution is available,how to verify that the solution is the global minimizer.For these problems,this thesis defines the sparsity and uniqueness,lists the available pursuit algorithms,and evaluates their performances.Finally, essence of the problem is that when the exact so- lution solving problem transits to the approximate solution solving problem,the related algorithms still work well.Based on this,we combine the K-complete orthogonal decomposition(K-COD)algorithm with orthogonal matching pursuit (OMP)algorithm to form the sparse representation(SR) noise suppression algo-rithm based on K-COD.Implement this algorithm to the empirical instances,to our knowledge,it is the better solution by far.●Chaotic signals are widely used in such as secure communication,optical fiber communication,and some other fields,however,they are vulnerable to be ad-ditive Gaussian white noise polluted.Since chaotic signal spectrum is similar to Gaussian white noise spectrum,the observed chaotic signal noise reduction task is considered difficult to achieve.Chaotic signals are initial sensitive;their patterns can not be learned by training.In addition,the sparsity of chaotic signals are insufficient,this limits the usage of the SR noise suppression algo-rithm based on K-COD.In this thesis,for that chaotic signal is different from the sparsely generated signal,as well as that chaotic signal can be reconstructed in phase space,we present a novel algorithm—local sparse representation (LSR) noise suppression algorithm.The LSR relies on applying SR locally to clusters of signals embedded in a high dimensional feature space of delayed coordinates. Compared with kernel principal component analysis(KPCA),local independent component analysis (LICA),and delayed algorithm for multiple unknown signals extraction (dAMUSE),LSR provides better noise suppression performance in the empirical experiments.We point out the advantages of the LSR, and gives cor-responding proof. From the proof, we conclude that LSR is a branch of the local regularization technique.●LSR relies on K-means clustering algorithm and SR based on K-COD.Their performances affect the performance of LSR. In K-means,it needs to predefine the number of clusters,and can not converge to the local maximum. For overcoming these shortages,we adopt the Density clustering 2.0 (DENCLUE 2.0)algorithm in this thesis.DENCLUE 2.0 relies on kernel density estimation based on Gaussian kernel,and has an improved hill climbing procedure.It determines the number of clusters automatically,adjusts the step size automatically at no extra costs, and converges to the local maximum exactly. For enhancing the SR performance requirements,this thesis presents a kernel fuzzy codebook estimation (KFCE) algorithm to generate SR dictionary from the observed data directly. Its basic idea is to integrate the distance kernel trick with the fuzzy clustering algorithm to generate dictionary for SR. We use the DENCLUE 2.0 and SR based on KFCE to improve LSR, and this forms the enhanced LSR(ELSR)algorithm.From experimental results,ELSR has better performance than the LSR.●After reviewing the SR noise suppression algorithm based on K-COD,LSR, and ELSR, we conclude that these algorithms pursuit better noise suppression per-formance.For processing the massive multimedia data, it usually decreases the performance level,and concentrates the computational speed.We enlighten from the previous demonstration,give an objective function based on maximum a pos-teriori (MAP)criterion. We propose a modified unscented Kalman filter (MUKF), whose principle is to integrate the advantage of square root unscented Kalman filter(SR-UKF) with that of the iterated unscented Kalman filter (IUKF),and utilize a modified measurement update procedure to achieve more accurate state estimation. We apply the MUKF to the MAP objective function, and then build the Fast MAP(FMAP)noise suppression algorithm. From experimental results, we find that FMAP match our design objectives,and it is suitable to be used in massive multimedia signals noise suppression.