A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition.Comment: 31 page

Blind source separation via independent and sparse component analysis with application to temporomandibular disorder

Blind source separation (BSS) addresses the problem of separating multi channel signals observed by generally spatially separated sensors into their constituent underlying sources. The passage of these sources through an unknown mixing medium results in these observed multichannel signals. This study focuses on BSS, with special emphasis on its application to the temporomandibular joint disorder (TMD). TMD refers to all medical problems related to the temporomandibular joint (TMJ), which holds the lower jaw (mandible) and the temporal bone (skull). The overall objective of the work is to extract the two TMJ sound sources generated by the two TMJs, from the bilateral recordings obtained from the auditory canals, so as to aid the clinician in diagnosis and planning treatment policies. Firstly, the concept of 'variable tap length' is adopted in convolutive blind source separation. This relatively new concept has attracted attention in the field of adaptive signal processing, notably the least mean square (LMS) algorithm, but has not yet been introduced in the context of blind signal separation. The flexibility of the tap length of the proposed approach allows for the optimum tap length to be found, thereby mitigating computational complexity or catering for fractional delays arising in source separation. Secondly, a novel fixed point BSS algorithm based on Ferrante's affine transformation is proposed. Ferrante's affine transformation provides the freedom to select the eigenvalues of the Jacobian matrix of the fixed point function and thereby improves the convergence properties of the fixed point iteration. Simulation studies demonstrate the improved convergence of the proposed approach compared to the well-known fixed point FastICA algorithm. Thirdly, the underdetermined blind source separation problem using a filtering approach is addressed. An extension of the FastICA algorithm is devised which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter achieves source recovery by employing the i-norm algorithm. Additionally, it will be shown that FastICA can also be utilised to extract the sources. Furthermore, it is illustrated how this scenario is particularly suitable for the separation of TMJ sounds. Finally, estimation of fractional delays between the mixtures of the TMJ sources is proposed as a means for TMJ separation. The estimation of fractional delays is shown to simplify the source separation to a case of in stantaneous BSS. Then, the estimated delay allows for an alignment of the TMJ mixtures, thereby overcoming a spacing constraint imposed by a well- known BSS technique, notably the DUET algorithm. The delay found from the TMJ bilateral recordings corroborates with the range reported in the literature. Furthermore, TMJ source localisation is also addressed as an aid to the dental specialist.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Blind source separation via independent and sparse component analysis with application to temporomandibular disorder

Blind source separation (BSS) addresses the problem of separating multi channel signals observed by generally spatially separated sensors into their constituent underlying sources. The passage of these sources through an unknown mixing medium results in these observed multichannel signals. This study focuses on BSS, with special emphasis on its application to the temporomandibular joint disorder (TMD). TMD refers to all medical problems related to the temporomandibular joint (TMJ), which holds the lower jaw (mandible) and the temporal bone (skull). The overall objective of the work is to extract the two TMJ sound sources generated by the two TMJs, from the bilateral recordings obtained from the auditory canals, so as to aid the clinician in diagnosis and planning treatment policies. Firstly, the concept of 'variable tap length' is adopted in convolutive blind source separation. This relatively new concept has attracted attention in the field of adaptive signal processing, notably the least mean square (LMS) algorithm, but has not yet been introduced in the context of blind signal separation. The flexibility of the tap length of the proposed approach allows for the optimum tap length to be found, thereby mitigating computational complexity or catering for fractional delays arising in source separation. Secondly, a novel fixed point BSS algorithm based on Ferrante's affine transformation is proposed. Ferrante's affine transformation provides the freedom to select the eigenvalues of the Jacobian matrix of the fixed point function and thereby improves the convergence properties of the fixed point iteration. Simulation studies demonstrate the improved convergence of the proposed approach compared to the well-known fixed point FastICA algorithm. Thirdly, the underdetermined blind source separation problem using a filtering approach is addressed. An extension of the FastICA algorithm is devised which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter achieves source recovery by employing the i-norm algorithm. Additionally, it will be shown that FastICA can also be utilised to extract the sources. Furthermore, it is illustrated how this scenario is particularly suitable for the separation of TMJ sounds. Finally, estimation of fractional delays between the mixtures of the TMJ sources is proposed as a means for TMJ separation. The estimation of fractional delays is shown to simplify the source separation to a case of in stantaneous BSS. Then, the estimated delay allows for an alignment of the TMJ mixtures, thereby overcoming a spacing constraint imposed by a well- known BSS technique, notably the DUET algorithm. The delay found from the TMJ bilateral recordings corroborates with the range reported in the literature. Furthermore, TMJ source localisation is also addressed as an aid to the dental specialist.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Blind source separation via independent and sparse component analysis with application to temporomandibular disorder

Blind source separation (BSS) addresses the problem of separating multi channel signals observed by generally spatially separated sensors into their constituent underlying sources. The passage of these sources through an unknown mixing medium results in these observed multichannel signals. This study focuses on BSS, with special emphasis on its application to the temporomandibular joint disorder (TMD). TMD refers to all medical problems related to the temporomandibular joint (TMJ), which holds the lower jaw (mandible) and the temporal bone (skull). The overall objective of the work is to extract the two TMJ sound sources generated by the two TMJs, from the bilateral recordings obtained from the auditory canals, so as to aid the clinician in diagnosis and planning treatment policies. Firstly, the concept of 'variable tap length' is adopted in convolutive blind source separation. This relatively new concept has attracted attention in the field of adaptive signal processing, notably the least mean square (LMS) algorithm, but has not yet been introduced in the context of blind signal separation. The flexibility of the tap length of the proposed approach allows for the optimum tap length to be found, thereby mitigating computational complexity or catering for fractional delays arising in source separation. Secondly, a novel fixed point BSS algorithm based on Ferrante's affine transformation is proposed. Ferrante's affine transformation provides the freedom to select the eigenvalues of the Jacobian matrix of the fixed point function and thereby improves the convergence properties of the fixed point iteration. Simulation studies demonstrate the improved convergence of the proposed approach compared to the well-known fixed point FastICA algorithm. Thirdly, the underdetermined blind source separation problem using a filtering approach is addressed. An extension of the FastICA algorithm is devised which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter achieves source recovery by employing the i-norm algorithm. Additionally, it will be shown that FastICA can also be utilised to extract the sources. Furthermore, it is illustrated how this scenario is particularly suitable for the separation of TMJ sounds. Finally, estimation of fractional delays between the mixtures of the TMJ sources is proposed as a means for TMJ separation. The estimation of fractional delays is shown to simplify the source separation to a case of in stantaneous BSS. Then, the estimated delay allows for an alignment of the TMJ mixtures, thereby overcoming a spacing constraint imposed by a well- known BSS technique, notably the DUET algorithm. The delay found from the TMJ bilateral recordings corroborates with the range reported in the literature. Furthermore, TMJ source localisation is also addressed as an aid to the dental specialist

Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio

Underdetermined blind separation by combining sparsity and independence of sources

In this paper, we address underdetermined blind separation of N sources from their M instantaneous mixtures, where N>M , by combining the sparsity and independence of sources. First, we propose an effective scheme to search some sample segments with the local sparsity, which means that in these sample segments, only Q(Q < M) sources are active. By grouping these sample segments into different sets such that each set has the same Q active sources, the original underdetermined BSS problem can be transformed into a series of locally overdetermined BSS problems. Thus, the blind channel identification task can be achieved by solving these overdetermined problems in each set by exploiting the independence of sources. In the second stage, we will achieve source recovery by exploiting a mild sparsity constraint, which is proven to be a sufficient and necessary condition to guarantee recovery of source signals. Compared with some sparsity-based UBSS approaches, this paper relaxes the sparsity restriction about sources to some extent by assuming that different source signals are mutually independent. At the same time, the proposed UBSS approach does not impose any richness constraint on sources. Theoretical analysis and simulation results illustrate the effectiveness of our approach