The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We...

Article history: Received 2 October 2016 Accepted 3 October 2016 Available online xxxx Presented by Haïm Brézis We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix t...

This paper proposes a new compression algorithm based on multi-scale learned bases. We first explain the construction of a set of image bases using a bintree segmentation and the optimization procedure used to select the image basis from this set. We then present the sparse orthonormal transforms introduced by Sezer et al. and propose some extensions tending to improve the convergence of the le...

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugatelinear symmetric operators...

This paper explores the segmentation of tutorial dialogue into cohesive topics. A latent semantic space was created using conversations from human to human tutoring transcripts, allowing cohesion between utterances to be measured using vector similarity. Previous cohesionbased segmentation methods that focus on expository monologue are reapplied to these dialogues to create benchmarks for perfo...

This paper appeared in the proceedings of ICASSP'95 bases can approximate it with only a few non-zero coefficients. It then becomes necessary to adaptively se-ABSTRACT lect an appropriate "best basis" which provides the best We propose a Best Basis Algorithm for Signal Enhance-signal estimate by discarding (thresholding) the noisy ment in white gaussian noise. We base our search of coefficients...