Multidimensional signal compression using multiscale recurrent patterns
Signal Processing - Image and Video Coding beyond Standards
Approximations with evolutionary pursuit
Signal Processing
Construction of Low Complexity Regular Quantizers for Overcomplete Expansions in RN
DCC '01 Proceedings of the Data Compression Conference
Quantized Oversampled Filter Banks with Erasures
DCC '01 Proceedings of the Data Compression Conference
Tight and sibling frames originated from discrete splines
Signal Processing
Robust multi-logo watermarking by RDWT and ICA
Signal Processing - Fractional calculus applications in signals and systems
Digital Signal Processing
Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
Quantization noise shaping on arbitrary frame expansions
EURASIP Journal on Applied Signal Processing
Characterization of oblique dual frame pairs
EURASIP Journal on Applied Signal Processing
EURASIP Journal on Applied Signal Processing
Foundations and Trends in Signal Processing
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
On the statistics of matching pursuit angles
Signal Processing
Uncertainty principles and vector quantization
IEEE Transactions on Information Theory
Greedy sparse signal reconstruction from sign measurements
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Analog beamforming in MIMO communications with phase shift networks and online channel estimation
IEEE Transactions on Signal Processing
Performance of sigma-delta quantizations in finite frames
IEEE Transactions on Information Theory
Image de-quantizing via enforcing sparseness in overcomplete representations
ACIVS'05 Proceedings of the 7th international conference on Advanced Concepts for Intelligent Vision Systems
On signal representations within the Bayes decision framework
Pattern Recognition
Constructing all self-adjoint matrices with prescribed spectrum and diagonal
Advances in Computational Mathematics
Hi-index | 754.96 |
Coefficient quantization has peculiar qualitative effects on representations of vectors in IR with respect to overcomplete sets of vectors. These effects are investigated in two settings: frame expansions (representations obtained by forming inner products with each element of the set) and matching pursuit expansions (approximations obtained by greedily forming linear combinations). In both cases, based on the concept of consistency, it is shown that traditional linear reconstruction methods are suboptimal, and better consistent reconstruction algorithms are given. The proposed consistent reconstruction algorithms were in each case implemented, and experimental results are included. For frame expansions, results are proven to bound distortion as a function of frame redundancy r and quantization step size for linear, consistent, and optimal reconstruction methods. Taken together, these suggest that optimal reconstruction methods will yield O(1/r2) mean-squared error (MSE), and that consistency is sufficient to insure this asymptotic behavior. A result on the asymptotic tightness of random frames is also proven. Applicability of quantized matching pursuit to lossy vector compression is explored. Experiments demonstrate the likelihood that a linear reconstruction is inconsistent, the MSE reduction obtained with a nonlinear (consistent) reconstruction algorithm, and generally competitive performance at low bit rates