Dictionary Learning Algorithms And Its Application In Speech Enhancement

Sparse redundant representation of signals,also referred to as sparse representation,means that signals can be represented by a linear combination of a few atoms(features).Sparse representation of signals can effectively extracts the inner-structure or features and reveals the main information.How to construct an effective dictionary is a key task for sparse representation.The more the dictionary matches the signals,the better(sparser)represent-tation we have.The most widely used way to generate a dictionary is analytical method,namely through some prespecified set of functions.However,this method requires a lot of expertise,while the structure of the dictionary is simple,not rich enough form.As the structures of the signals that need to be represented become more and more complex,the dictionary designed by hand has been unable to meet the actual needs.Therefore,we hope that we can automatically learn a dictionary which adaptively matches the signals from the large-scale training samples(signals),so that the representation of the samples is more sparse.Dictionary learning is the tool to solve this problem.This thesis focuses on dictionary learning algorithms.We compare the existing methods and present our new algorithm and apply it to speech enhancement.First,the theory and experimental analysis of the dictionary learning algorithms.In this part,this thesis makes a systematic theoretical comparison and experimental analysis of the existing dictionary learning algorithms.From the theoretical point of view,we introduce the principle of all the algorithms,figure out the relationship between them,and find their differences from the perspective of objective function.In our experiments,we analyze three key points in improving dictionary learning algorithms,including the update idea,the update method,and the regularization term.We evaluate dictionary learning algorithms with two experiments on recovering a known synthetic dictionary and sparsel y approximating a class of auto-regressive signals,and we argue that they cover the necessary abilities of a good dictionary learning algorithm.Through theory and practical experiments,we present some guidelines for how to improve dictionary learning algorithms.Second,the improvement and simulation based on One-Stage Dictionary Learning(OS-DL)algorithm.We find that the existing dictionary learning algorithms often do not have any constraints on the dictionary,causing overshooting problems,and so as the OS-DL algorithm.To solve this problem,this thesis improves the OS-DL algorithm and proposes a Bounded One-Stage Dictionary Learning(BOS-DL)algorithm.This algorithm adds the constraint of L2-norm to the dictionary,preserves the advantages of OS-DL algorithm and improves the stability.Experimental results on synthetic signals and autoregressive signals demonstrate the promising performance of the proposed algorithms.Third,the speech enhancement method based on BOS-DL algorithm.In this part,this thesis analyzes the existing speech enhancement method based on K-SVD algorithm.We point out the drawbacks of these methods and present our new method based on BOS-DL algorithm.This method overcomes the problem of large computational complexity of K-SVD algorithm.In the TIMIT speech database,the experimental results show that our method is 2 to 3 times less time than the speech enhancement method based on K-SVD algorithm,and can achieve better enhancement effect.