Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory

Sparse Representations Are Most Likely to Be the Sparsest Possible

Given a signal and a full-rank matrix with

Authors: Michael Elad

Characterization of Oblique Dual Frame Pairs

Given a frame for a subspace of a Hilbert space , we consider...

Authors: Yonina C. Eldar and Ole Christensen

Frames and Overcomplete Representations in Signal Processing, Communications, and Information Theory

Authors: Radu V. Balan, Yonina C. Eldar and Thomas Strohmer

A Unified Transform for LTI Systems—Presented as a (Generalized) Frame

We present a set of functions in and show it to be a (tight) generalized frame (as presented by G. Kaiser (1994)). The analysis side of ...

Authors: Arie Feuer, Paul M.J. Van den Hof and Peter S.C. Heuberger

The Finite Heisenberg-Weyl Groups in Radar and Communications

We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We co...

Authors: S. D. Howard, A. R. Calderbank and W. Moran

Joint Source-Channel Coding by Means of an Oversampled Filter Bank Code

Quantized frame expansions based on block transforms and oversampled filter banks (OFBs) have been considered recently as joint source-channel codes (JSCCs) for erasure and error-resilient signal transmission ...

Authors: Slavica Marinkovic and Christine Guillemot

Wavelet Video Denoising with Regularized Multiresolution Motion Estimation

This paper develops a new approach to video denoising, in which motion estimation/compensation, temporal filtering, and spatial smoothing are all undertaken in the wavelet domain. The key to making this possible ...

Authors: Fu Jin, Paul Fieguth and Lowell Winger

Fourier Transforms of Finite Chirps

Chirps arise in many signal processing applications. While chirps have been extensively studied as functions over both the real line and the integers, less attention has been paid to the study of chirps over f...

Authors: Peter G. Casazza and Matthew Fickus

Facial Image Compression Based on Structured Codebooks in Overcomplete Domain

We advocate facial image compression technique in the scope of distributed source coding framework. The novelty of the proposed approach is twofold: image compression is considered from the position of source ...

Authors: J. E. Vila-Forcén, S. Voloshynovskiy, O. Koval and T. Pun

An Overcomplete Signal Basis Approach to Nonlinear Time-Tone Analysis with Application to Audio and Speech Processing

Although a beating tone and the two pure tones which give rise to it are linearly dependent, the ear considers them to be independent as tone sensations. A linear time-frequency representation of acoustic data...

Authors: Richard B. Reilly

Reconstruction of Nonuniformly Sampled Bandlimited Signals by Means of Time-Varying Discrete-Time FIR Filters

This paper deals with reconstruction of nonuniformly sampled bandlimited continuous-time signals using time-varying discrete-time finite-length impulse response (FIR) filters. The main theme of the paper is to...

Authors: Håkan Johansson and Per Löwenborg

Quantization Noise Shaping on Arbitrary Frame Expansions

Quantization noise shaping is commonly used in oversampled A/D and D/A converters with uniform sampling. This paper considers quantization noise shaping for arbitrary finite frame expansions based on generaliz...

Authors: Petros T. Boufounos and Alan V. Oppenheim

Frame-Based Multiple-Description Video Coding with Extended Orthogonal Filter Banks

We propose a frame-based multiple-description video coder. The analysis filter bank is the extension of an orthogonal filter bank which computes the spatial polyphase components of the original video frames. T...

Authors: R. Bernardini, M. Durigon, R. Rinaldo, A. Vitali and P. Zontone

Texture Classification Using Sparse Frame-Based Representations

A new method for supervised texture classification, denoted by frame texture classification method (FTCM), is proposed. The method is based on a deterministic texture model in which a small image block, taken ...

Authors: Karl Skretting and JohnHåkon Husøy

Geometric Properties of Grassmannian Frames for and

Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for two- and three-dimensional Euclidean space ( ...

Authors: John J Benedetto and Joseph D Kolesar

Simplified Design of Low-Delay Oversampled NPR GDFT Filterbanks

We propose an efficient algorithm for designing the prototype filters of oversampled, near-perfect reconstruction (NPR), GDFT modulated filterbanks (FB) with arbitrary delay. We describe simplified conditions ...

Authors: Bogdan Dumitrescu, Robert Bregović and Tapio Saramäki

Paraunitary Oversampled Filter Bank Design for Channel Coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-base...

Authors: Stephan Weiss, Soydan Redif, Tom Cooper, Chunguang Liu, Paul D Baxter and John G McWhirter

Denoising by Sparse Approximation: Error Bounds Based on Rate-Distortion Theory

If a signal is known to have a sparse representation with respect to a frame, it can be estimated from a noise-corrupted observation

Authors: Alyson K Fletcher, Sundeep Rangan, Vivek K Goyal and Kannan Ramchandran

The Hermite Transform: A Survey

With this survey on the Hermite transformation we want to pursue the following two goals. First, we want to provide a comprehensive and up-to-date description of the Hermite transformation, its underlying phil...

Authors: Jean-Bernard Martens

Wireless Multicarrier Communications via Multipulse Gabor Riesz Bases

We introduce multipulse multicarrier (MPMC) modulation, a wireless communication scheme that augments traditional single-pulse multicarrier systems by using multiple pulses at the transmitter and the receiver. Th...

Authors: Manfred M Hartmann, Gerald Matz and Dieter Schafhuber

A Packetized SPIHT Algorithm with Overcomplete Wavelet Coefficients for Increased Robustness

This paper presents a wavelet-based image encoding scheme with error resilience and error concealment suitable for transmission over networks prone to packet losses. The scheme involves partitioning the data i...

Authors: Y Sriraja and Tanja Karp

Perfect Reconstruction Conditions and Design of Oversampled DFT-Modulated Transmultiplexers

This paper presents a theoretical analysis of oversampled complex modulated transmultiplexers. The perfect reconstruction (PR) conditions are established in the polyphase domain for a pair of biorthogonal prot...

Authors: Cyrille Siclet, Pierre Siohan and Didier Pinchon