NMF-based compositional models for audio source separation

Abstract

Many classes of data can be represented by constructive combinations of parts. Most signal and data from nature have nonnegative values and can be explained and reconstructed by constructive models. By the constructive models, only the additive combination is allowed and it does not result in subtraction of parts. The compositional models include dictionary learning, exemplar-based approaches, and nonnegative matrix factorization (NMF). Compositional models are desirable in many areas including image or visual signal processing, text information processing, audio signal processing, and music information retrieval. In this dissertation, we choose NMF for compositional models and NMF-based target source separation is performed for the application. The target source separation is the extraction or reconstruction of the target signals in the mixture signals which consists with the target and interfering signals. The target source separation can be thought as blind source separation (BSS). BSS aims that the original unknown source signals are extracted without knowing or with very limited information. However, in these days, much of prior information is frequently utilized, and various approaches have been proposed for single channel source separation. NMF basically approximates a nonnegative data matrix V with a product of nonnegative basis and encoding matrices W and H, i.e., V WH. Since both W and H are nonnegative, NMF often leads to a part based representation of the data. The methods based on NMF have shown impressive results in single channel source separation The objective function of NMF is generally presented Euclidean distant, Kullback-Leibler divergence, and Itakura-saito divergence. Many optimization methods have been proposed and utilized, e.g., multiplicative update rule, projected gradient descent and NeNMF. However, NMF-based audio source separation has some issues as follows: non-uniqueness of the bases, a high dependence to the prior information, the overlapped subspace between target bases and interfering bases, a disregard of the encoding vectors from the training phase, and insucient analysis of sparse NMF. In this dissertation, we propose new approaches to resolve the above issues. In section 4, we propose a novel speech enhancement method that combines the statistical model-based enhancement scheme with the NMF-based gain function. For a better performance in time-varying noise environments, both the speech and noise bases of NMF are adapted simultaneously with the help of the estimated speech presence probability. In section 5, we propose a discriminative NMF (DNMF) algorithm which exploits the reconstruction error for the interfering signals as well as the target signal based on target bases. In section 6, we propose an approach to robust bases estimation in which an incremental strategy is adopted. Based on an analogy between clustering and NMF analysis, we incrementally estimate the NMF bases similar to the modied k-means and Linde-Buzo-Gray algorithms popular in the data clustering area. In Section 7, the distribution of the encoding vector is modeled as a multivariate exponential PDF (MVE) with a single scaling factor for each source. In Section 8, several sparse penalty terms for NMF are analyzed and compared in terms of signal to distortion ratio, sparseness of encoding vectors, reconstruction error, and entropy of basis vectors. The new objective function which applied sparse representation and discriminative NMF (DNMF) is also proposed.