Systematic construction of real lapped tight frame transforms

Authors:
Aliaksei Sandryhaila;Amina Chebira;Christina Milo;Jelena Kovačević;Markus Püschel
Affiliations:
Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA;School of Computer and Communications Science, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland;Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA;Departments of Electrical and Computer Engineering and Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA;Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.