Independent Process Analysis without A Priori Dimensional Information

Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes. Our claim is supported by numerical simulations. As a particular application, we search for subspaces of facial components.Comment: 9 pages, 2 figure

On the stable recovery of the sparsest overcomplete representations in presence of noise

Let x be a signal to be sparsely decomposed over a redundant dictionary A, i.e., a sparse coefficient vector s has to be found such that x=As. It is known that this problem is inherently unstable against noise, and to overcome this instability, the authors of [Stable Recovery; Donoho et.al., 2006] have proposed to use an "approximate" decomposition, that is, a decomposition satisfying ||x - A s|| < \delta, rather than satisfying the exact equality x = As. Then, they have shown that if there is a decomposition with ||s||_0 < (1+M^{-1})/2, where M denotes the coherence of the dictionary, this decomposition would be stable against noise. On the other hand, it is known that a sparse decomposition with ||s||_0 < spark(A)/2 is unique. In other words, although a decomposition with ||s||_0 < spark(A)/2 is unique, its stability against noise has been proved only for highly more restrictive decompositions satisfying ||s||_0 < (1+M^{-1})/2, because usually (1+M^{-1})/2 << spark(A)/2. This limitation maybe had not been very important before, because ||s||_0 < (1+M^{-1})/2 is also the bound which guaranties that the sparse decomposition can be found via minimizing the L1 norm, a classic approach for sparse decomposition. However, with the availability of new algorithms for sparse decomposition, namely SL0 and Robust-SL0, it would be important to know whether or not unique sparse decompositions with (1+M^{-1})/2 < ||s||_0 < spark(A)/2 are stable. In this paper, we show that such decompositions are indeed stable. In other words, we extend the stability bound from ||s||_0 < (1+M^{-1})/2 to the whole uniqueness range ||s||_0 < spark(A)/2. In summary, we show that "all unique sparse decompositions are stably recoverable". Moreover, we see that sparser decompositions are "more stable".Comment: Accepted in IEEE Trans on SP on 4 May 2010. (c) 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other work

Independent component analysis and source analysis of auditory evoked potentials for assessment of cochlear implant users

Source analysis of the Auditory Evoked Potential (AEP) has been used before to evaluate the maturation of the auditory system in both adult and children; in the same way, this technique could be applied to ongoing EEG recordings, in response to acoustic specific frequency stimuli, from children with cochlear implants (CI). This is done in oder to objectively assess the performance of this electronic device and the maturation of the child?s hearing. However, these recordings are contaminated by an artifact produced by the normal operation of the CI; this artifact in particular makes the detection and analysis of AEPs much harder and generates errors in the source analysis process. The artifact can be spatially filtered using Independent Component Analysis (ICA); in this research, three different ICA algorithms were compared in order to establish the more suited algorithm to remove the CI artifact. Additionally, we show that pre-processing the EEG recording, using a temporal ICA algorithm, facilitates not only the identification of the AEP peaks but also the source analysis procedure. From results obtained in this research and limited dataset of CI vs normal recordings, it is possible to conclude that the AEPs source locations change from the inferior temporal areas in the first 2 years after implantation to the superior temporal area after three years using the CIs, close to the locations obtained in normal hearing children. It is intended that the results of this research are used as an objective technique for a general evaluation of the performance of children with CIs