Non-negative matrix factorization with mixture of Itakura-Saito divergence for SAR images

Synthetic aperture radar (SAR) data are becoming more and more accessible and have been widely used in many applications. To effectively and efficiently represent multiple SAR images, we propose the mixture of Itakura-Saito (IS) divergence for non-negative matrix factorization (NMF) to perform the dimension reduction. Our proposed method incorporates the unit-mean Gamma mixture model into the NMF to model the multiplicative noise. To obtain the closed-form update equations as much as possible, we approximate the log-likelihood function with its lower bound. Finally, we apply Expectation-Maximization (EM) algorithm to estimate the parameters, resulting in the closed-form multiplicative update rules for the two matrix factors. Experimental results on real SAR dataset demonstrate the effectiveness of the proposed method and its applicability to post applications (e.g., classification) with improved performances over the conventional dimension reduction methods

Statistical single channel source separation

PhD ThesisSingle channel source separation (SCSS) principally is one of the challenging fields in signal processing and has various significant applications. Unlike conventional SCSS methods which were based on linear instantaneous model, this research sets out to investigate the separation of single channel in two types of mixture which is nonlinear instantaneous mixture and linear convolutive mixture. For the nonlinear SCSS in instantaneous mixture, this research proposes a novel solution based on a two-stage process that consists of a Gaussianization transform which efficiently compensates for the nonlinear distortion follow by a maximum likelihood estimator to perform source separation. For linear SCSS in convolutive mixture, this research proposes new methods based on nonnegative matrix factorization which decomposes a mixture into two-dimensional convolution factor matrices that represent the spectral basis and temporal code. The proposed factorization considers the convolutive mixing in the decomposition by introducing frequency constrained parameters in the model. The method aims to separate the mixture into its constituent spectral-temporal source components while alleviating the effect of convolutive mixing. In addition, family of Itakura-Saito divergence has been developed as a cost function which brings the beneficial property of scale-invariant. Two new statistical techniques are proposed, namely, Expectation-Maximisation (EM) based algorithm framework which maximizes the log-likelihood of a mixed signals, and the maximum a posteriori approach which maximises the joint probability of a mixed signal using multiplicative update rules. To further improve this research work, a novel method that incorporates adaptive sparseness into the solution has been proposed to resolve the ambiguity and hence, improve the algorithm performance. The theoretical foundation of the proposed solutions has been rigorously developed and discussed in details. Results have concretely shown the effectiveness of all the proposed algorithms presented in this thesis in separating the mixed signals in single channel and have outperformed others available methods.Universiti Teknikal Malaysia Melaka(UTeM), Ministry of Higher Education of Malaysi

Blind source separation using statistical nonnegative matrix factorization

PhD ThesisBlind Source Separation (BSS) attempts to automatically extract and track a signal of interest in real world scenarios with other signals present. BSS addresses the problem of recovering the original signals from an observed mixture without relying on training knowledge. This research studied three novel approaches for solving the BSS problem based on the extensions of non-negative matrix factorization model and the sparsity regularization methods. 1) A framework of amalgamating pruning and Bayesian regularized cluster nonnegative tensor factorization with Itakura-Saito divergence for separating sources mixed in a stereo channel format: The sparse regularization term was adaptively tuned using a hierarchical Bayesian approach to yield the desired sparse decomposition. The modified Gaussian prior was formulated to express the correlation between different basis vectors. This algorithm automatically detected the optimal number of latent components of the individual source. 2) Factorization for single-channel BSS which decomposes an information-bearing matrix into complex of factor matrices that represent the spectral dictionary and temporal codes: A variational Bayesian approach was developed for computing the sparsity parameters for optimizing the matrix factorization. This approach combined the advantages of both complex matrix factorization (CMF) and variational -sparse analysis. BLIND SOURCE SEPARATION USING STATISTICAL NONNEGATIVE MATRIX FACTORIZATION ii 3) An imitated-stereo mixture model developed by weighting and time-shifting the original single-channel mixture where source signals can be modelled by the AR processes. The proposed mixing mixture is analogous to a stereo signal created by two microphones with one being real and another virtual. The imitated-stereo mixture employed the nonnegative tensor factorization for separating the observed mixture. The separability analysis of the imitated-stereo mixture was derived using Wiener masking. All algorithms were tested with real audio signals. Performance of source separation was assessed by measuring the distortion between original source and the estimated one according to the signal-to-distortion (SDR) ratio. The experimental results demonstrate that the proposed uninformed audio separation algorithms have surpassed among the conventional BSS methods; i.e. IS-cNTF, SNMF and CMF methods, with average SDR improvement in the ranges from 2.6dB to 6.4dB per source.Payap Universit

Improved Convolutive and Under-Determined Blind Audio Source Separation with MRF Smoothing

Convolutive and under-determined blind audio source separation from noisy recordings is a challenging problem. Several computational strategies have been proposed to address this problem. This study is concerned with several modifications to the expectation-minimization-based algorithm, which iteratively estimates the mixing and source parameters. This strategy assumes that any entry in each source spectrogram is modeled using superimposed Gaussian components, which are mutually and individually independent across frequency and time bins. In our approach, we resolve this issue by considering a locally smooth temporal and frequency structure in the power source spectrograms. Local smoothness is enforced by incorporating a Gibbs prior in the complete data likelihood function, which models the interactions between neighboring spectrogram bins using a Markov random field. Simulations using audio files derived from stereo audio source separation evaluation campaign 2008 demonstrate high efficiency with the proposed improvement

Multichannel audio source separation with deep neural networks

International audienceThis article addresses the problem of multichannel audio source separation. We propose a framework where deep neural networks (DNNs) are used to model the source spectra and combined with the classical multichannel Gaussian model to exploit the spatial information. The parameters are estimated in an iterative expectation-maximization (EM) fashion and used to derive a multichannel Wiener filter. We present an extensive experimental study to show the impact of different design choices on the performance of the proposed technique. We consider different cost functions for the training of DNNs, namely the probabilistically motivated Itakura-Saito divergence, and also Kullback-Leibler, Cauchy, mean squared error, and phase-sensitive cost functions. We also study the number of EM iterations and the use of multiple DNNs, where each DNN aimsto improve the spectra estimated by the preceding EM iteration. Finally, we present its application to a speech enhancement problem. The experimental results show the benefit of the proposed multichannel approach over a single-channel DNN-based approach and the conventional multichannel nonnegative matrix factorization based iterative EM algorithm

Single channel blind source separation

Single channel blind source separation (SCBSS) is an intensively researched field with numerous important applications. This research sets out to investigate the separation of monaural mixed audio recordings without relying on training knowledge. This research proposes a novel method based on variable regularised sparse nonnegative matrix factorization which decomposes an information-bearing matrix into two-dimensional convolution of factor matrices that represent the spectral basis and temporal code of the sources. In this work, a variational Bayesian approach has been developed for computing the sparsity parameters of the matrix factorization. To further improve the previous work, this research proposes a new method based on decomposing the mixture into a series of oscillatory components termed as the intrinsic mode functions (IMF). It is shown that IMFs have several desirable properties unique to SCBSS problem and how these properties can be advantaged to relax the constraints posed by the problem. In addition, this research develops a novel method for feature extraction using psycho-acoustic model. The monaural mixed signal is transformed to a cochleagram using the gammatone filterbank, whose bandwidths increase incrementally as the center frequency increases; thus resulting to non-uniform time-frequency (TF) resolution in the analysis of audio signal. Within this domain, a family of Itakura-Saito (IS) divergence based novel two-dimensional matrix factorization has been developed. The proposed matrix factorizations have the property of scale invariant which enables lower energy components in the cochleagram to be treated with equal importance as the high energy ones. Results show that all the developed algorithms presented in this thesis have outperformed conventional methods.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Projection-based demixing of spatial audio

International audienceWe propose a method to unmix multichannel audio signals into their different constitutive spatial objects. To achievethis, we characterize an audio object through both a spatial and a spectro-temporal modelling. The particularity of the spatialmodel we pick is that it neither assumes an object has only one underlying source point, nor does it attempt to model the complexroom acoustics. Instead, it focuses on a listener perspective, and takes each object as the superposition of many contributionswith different incoming directions and inter-channel delays. Our spectro-temporal probabilistic model is based on the recentlyproposed α-harmonisable processes, which are adequate for signals with large dynamics, such as audio. Then, the mainoriginality of this work is to provide a new way to estimate and exploit inter-channel dependences of an object for the purposeof demixing. In the Gaussian α = 2 case, previous research focused on covariance structures. This approach is no longervalid for α < 2 where covariances are not defined. Instead, we show how simple linear combinations of the mixture channelscan be used to learn the model parameters, and the method we propose consists in pooling the estimates based on manyprojections to correctly account for the original multichannel audio. Intuitively, each such downmix of the mixture provides anew perspective where some objects are cancelled or enhanced. Finally, we also explain how to recover the different spatial audioobjects when all parameters have been computed. Performance of the method is illustrated on the separation of stereophonic musicsignals. Index Terms—source separation, probabilistic models, non-negative matrix factorization, musical source separatio

Generalization of the K-SVD algorithm for minimization of ß-divergence

[EN] In this paper, we propose, describe, and test a modification of the K-SVD algorithm. Given a set of training data, the proposed algorithm computes an overcomplete dictionary by minimizing the ß-divergence () between the data and its representation as linear combinations of atoms of the dictionary, under strict sparsity restrictions. For the special case , the proposed algorithm minimizes the Frobenius norm and, therefore, for the proposed algorithm is equivalent to the original K-SVD algorithm. We describe the modifications needed and discuss the possible shortcomings of the new algorithm. The algorithm is tested with random matrices and with an example based on speech separation.This work has been partially supported by the EU together with the Spanish Government through TEC2015-67387-C4-1-R (MINECO/FEDER) and by Programa de FPU del Ministerio de Educacion, Cultura y Deporte FPU13/03828 (Spain).García Mollá, VM.; San Juan-Sebastian, P.; Virtanen, T.; Vidal Maciá, AM.; Alonso-Jordá, P. (2019). Generalization of the K-SVD algorithm for minimization of ß-divergence. Digital Signal Processing. 92:47-53. https://doi.org/10.1016/j.dsp.2019.05.001S47539