Maria G. Jafari

Audio Inpainting

We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.

Fetal electrocardiogram extraction by sequential source separation in the wavelet domain

This work addresses the problem of fetal electrocardiogram extraction using blind source separation (BSS) in the wavelet domain. A new approach is proposed, which is particularly advantageous when the mixing environment is noisy and time-varying, and that is shown, analytically and in simulation, to improve the convergence rate of the natural gradient algorithm. The distribution of the wavelet coefficients of the source signals is then modeled by a generalized Gaussian probability density, whereby in the time-scale domain the problem of selecting appropriate nonlinearities when separating mixtures of both sub- and super-Gaussian signals is mitigated, as shown by experimental results.

Fast Dictionary Learning for Sparse Representations of Speech Signals

For dictionary-based decompositions of certain types, it has been observed that there might be a link between sparsity in the dictionary and sparsity in the decomposition. Sparsity in the dictionary has also been associated with the derivation of fast and efficient dictionary learning algorithms. Therefore, in this paper we present a greedy adaptive dictionary learning algorithm that sets out to find sparse atoms for speech signals. The algorithm learns the dictionary atoms on data frames taken from a speech signal. It iteratively extracts the data frame with minimum sparsity index, and adds this to the dictionary matrix. The contribution of this atom to the data frames is then removed, and the process is repeated. The algorithm is found to yield a sparse signal decomposition, supporting the hypothesis of a link between sparsity in the decomposition and dictionary. The algorithm is applied to the problem of speech representation and speech denoising, and its performance is compared to other existing methods. The method is shown to find dictionary atoms that are sparser than their time-domain waveform, and also to result in a sparser speech representation. In the presence of noise, the algorithm is found to have similar performance to the well established principal component analysis.

Sequential blind source separation based exclusively on second-order statistics developed for a class of periodic signals

A sequential algorithm for the blind separation of a class of periodic source signals is introduced in this paper. The algorithm is based only on second-order statistical information and exploits the assumption that the source signals have distinct periods. Separation is performed by sequentially converging to a solution which in effect diagonalizes the output covariance matrix constructed at a lag corresponding to the fundamental period of the source we select, the one with the smallest period. Simulation results for synthetic signals and real electrocardiogram recordings show that the proposed algorithm has the ability to restore statistical independence, and its performance is comparable to that of the equivariant adaptive source separation (EASI) algorithm, a benchmark high-order statistics-based sequential algorithm with similar computational complexity. The proposed algorithm is also shown to mitigate the limitation that the EASI algorithm can separate at most one Gaussian distributed source. Furthermore, the steady-state performance of the proposed algorithm is compared with that of EASI and the block-based second-order blind identification (SOBI) method.

A constrained matching pursuit approach to audio declipping

We present a novel sparse representation based approach for the restoration of clipped audio signals. In the proposed approach, the clipped signal is decomposed into overlapping frames and the declipping problem is formulated as an inverse problem, per audio frame. This problem is further solved by a constrained matching pursuit algorithm, that exploits the sign pattern of the clipped samples and their maximal absolute value. Performance evaluation with a collection of music and speech signals demonstrate superior results compared to existing algorithms, over a wide range of clipping levels.

Sparse coding for convolutive blind audio source separation

In this paper, we address the convolutive blind source separation (BSS) problem with a sparse independent component analysis (ICA) method, which uses ICA to find a set of basis vectors from the observed data, followed by clustering to identify the original sources. We show that, thanks to the temporally localised basis vectors that result, phase information is easily exploited to determine the clusters, using an unsupervised clustering method. Experimental results show that good performance is obtained with the proposed approach, even for short basis vectors.

Analysis-based sparse reconstruction with synthesis-based solvers

Analysis based reconstruction has recently been introduced as an alternative to the well-known synthesis sparsity model used in a variety of signal processing areas. In this paper we convert the analysis exact-sparse reconstruction problem to an equivalent synthesis recovery problem with a set of additional constraints. We are therefore able to use existing synthesis-based algorithms for analysis-based exact-sparse recovery. We call this the Analysis-By-Synthesis (ABS) approach. We evaluate our proposed approach by comparing it against the recent Greedy Analysis Pursuit (GAP) analysis-based recovery algorithm. The results show that our approach is a viable option for analysis-based reconstruction, while at the same time allowing many algorithms that have been developed for synthesis reconstruction to be directly applied for analysis reconstruction as well.

An adaptive stereo basis method for convolutive blind audio source separation

We consider the problem of convolutive blind source separation of stereo mixtures, where a pair of microphones records mixtures of sound sources that are convolved with the impulse response between each source and sensor. We propose an adaptive stereo basis (ASB) source separation method for such convolutive mixtures, using an adaptive transform basis which is learned from the stereo mixture pair. The stereo basis vector pairs of the transform are grouped according to the estimated relative delay between the left and right channels for each basis, and the sources are then extracted by projecting the transformed signal onto the subspace corresponding to each group of basis vector pairs. The performance of the proposed algorithm is compared with FD-ICA and DUET under different reverberation and noise conditions, using both objective distortion measures and formal listening tests. The results indicate that the proposed stereo coding method is competitive with both these algorithms at short and intermediate reverberation times, and offers significantly improved performance at low noise and short reverberation times.

A combined Kalman filter and natural gradient algorithm approach for blind separation of binary distributed sources in time-varying channels

A combined Kalman filter (KF) and natural gradient algorithm (NGA) approach is proposed to address the problem of blind source separation (BSS) in time-varying environments, in particular for binary distributed signals. In situations where the mixing channel is nonstationary, the performance of the NGA is often poor. Typically, in such cases, an adaptive learning rate is used to help the NGA track the changes in the environment. The Kalman filter, on the other hand, is the optimal, minimum mean square error method for tracking certain non-stationarity. Experimental results are presented, and suggest that the combined approach performs significantly better than NGA in the presence of both continuous and abrupt non-stationarities.

Denoising and segmentation of the second heart sound using matching pursuit

We propose a denoising and segmentation technique for the second heart sound (S2). To denoise, Matching Pursuit (MP) was applied using a set of non-linear chirp signals as atoms. We show that the proposed method can be used to segment the phonocardiogram of the second heart sound into its two clinically meaningful components: the aortic (A2) and pulmonary (P2) components.