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 un­ known mixing medium results in these observed multichannel signals. This study focuses on BSS, with special emphasis on its application to the tem­ poromandibular 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 TM J 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) al­ gorithm, 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 Jacobi an 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 algo­ rithm. 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 em­ ploying 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 TM J 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 wellknown BSS technique, notably the DUET algorithm. The delay found from the TM J bilateral recordings corroborates with the range reported in the literature. Furthermore, TM J source localisation is also addressed as an aid to the dental specialist.