Advances in multirate filter bank structures and multiscale representations

We propose a new framework to extract the activity-related component in the BOLD functional Magnetic Resonance Imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparsely-distributed stimuli, as is the case in slow event-related fMRI. We introduce new wavelet bases, termed "activelets'', which sparsify the activity-related BOLD signal. These wavelets mimic the behavior of the differential operator underlying the hemodynamic system. To recover the sparse representation, we deploy a sparse-solution search algorithm. The feasibility of the method is evaluated using both synthetic and experimental fMRI data. The importance of the activelet basis and the non-linear sparse recovery algorithm is demonstrated by comparison against classical Bspline wavelets and linear regularization, respectively. Fast orthogonal sparse approximation algorithms over local dictionaries B. Mailhé, R. Gribonval, P. Vandergheynst, F. Bimbot Abstract: In this work we present a new greedy algorithm for sparse approximation called LocOMP. LocOMP is meant to be run on local dictionaries made of atoms with much shorter supports than the signal length. This notably encompasses shift-invariant dictionaries and time-frequency dictionaries, be they monoscale or multiscale. In this case, very fast implementations of Matching Pursuit are already available. LocOMP is almost as fast as Matching Pursuit In this work we present a new greedy algorithm for sparse approximation called LocOMP. LocOMP is meant to be run on local dictionaries made of atoms with much shorter supports than the signal length. This notably encompasses shift-invariant dictionaries and time-frequency dictionaries, be they monoscale or multiscale. In this case, very fast implementations of Matching Pursuit are already available. LocOMP is almost as fast as Matching Pursuit while approaching the signal almost as well as the much slower Orthogonal Matching Pursuit. Recursive Nearest Neighbor Search in a Sparse and Multiscale Domain for Comparing Audio Signals B. Sturm, L. Daudet Abstract: We investigate recursive nearest neighbor search in a sparse domain at the scale of audio signals. Essentially, to approximate the cosine distance between the signals we make pairwise comparisons between the elements of localized sparse models built from large and redundant multiscale dictionaries of time-frequency atoms. Theoretically, error bounds on these approximations provide efficient means for quickly reducing the search space to the nearest We investigate recursive nearest neighbor search in a sparse domain at the scale of audio signals. Essentially, to approximate the cosine distance between the signals we make pairwise comparisons between the elements of localized sparse models built from large and redundant multiscale dictionaries of time-frequency atoms. Theoretically, error bounds on these approximations provide efficient means for quickly reducing the search space to the nearest neighborhood of a given data; but we demonstrate here that the tightest bound involving a probabilistic assumption does not provide a practical approach for comparing audio signals with respect to this distance measure. Our experiments show, however, that regardless of these non-discriminative bounds, we only need to make a few atom pair comparisons to reveal, e.g., the position of origin of an excerpted signal, or melodies with similar time-frequency structures. Symmetric Tight Frame Wavelets With Dilation Factor M=4 F. Abdelnour Abstract: In this paper we discuss a new set of symmetric tight frame wavelets with the associated filterbank outputs downsampled by four at each stage. The frames consist of seven generators obtained from the lowpass filter using spectral factorization, with the lowpass filter obtained via Groebner basis method. The filters are simple to construct, and offer smooth scaling functions and wavelets. Additionally, the filterbanks presented in this paper have limited redundancy while maintaining the smoothness of underlying limit functions. The filters are linear phase (symmetric), FIR, and the resulting wavelets possess vanishing moments.