Continuous and discrete wavelet transforms
SIAM Review
Vector quantization and signal compression
Vector quantization and signal compression
Multirate systems and filter banks
Multirate systems and filter banks
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Multi-frame compression: theory and design
Signal Processing - Special section on signal processing technologies for short burst wireless communications
Subband Compression of Images: Principals and Examples
Subband Compression of Images: Principals and Examples
Road Sign Interpretation Using Matching Pursuit Method
SSIAI '00 Proceedings of the 4th IEEE Southwest Symposium on Image Analysis and Interpretation
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 1)-Volume 1 - Volume 1
Learning Overcomplete Representations
Neural Computation
IEEE Transactions on Signal Processing
Frame-theoretic analysis of oversampled filter banks
IEEE Transactions on Signal Processing
Fast matching pursuit with a multiscale dictionary of Gaussianchirps
IEEE Transactions on Signal Processing
Optimized signal expansions for sparse representation
IEEE Transactions on Signal Processing
Stochastic time-frequency dictionaries for matching pursuit
IEEE Transactions on Signal Processing
A fast globally optimal algorithm for template matching using low-resolution pruning
IEEE Transactions on Image Processing
A selective update approach to matching pursuits video coding
IEEE Transactions on Circuits and Systems for Video Technology
Very low bit-rate video coding based on matching pursuits
IEEE Transactions on Circuits and Systems for Video Technology
Subband dictionaries for low-cost matching pursuits of video residues
IEEE Transactions on Circuits and Systems for Video Technology
Modulus quantization for matching-pursuit video coding
IEEE Transactions on Circuits and Systems for Video Technology
Digital Signal Processing
Recursive least squares dictionary learning algorithm
IEEE Transactions on Signal Processing
An application of Newton's method in wireless systems
Proceedings of the 8th International Conference on Frontiers of Information Technology
Decomposition and dictionary learning for 3D trajectories
Signal Processing
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Signal expansions using frames may be considered as generalizations of signal representations based on transforms and filter banks. Frames, or dictionaries, for sparse signal representations may be designed using an iterative algorithm with two main steps: (1) Frame vector selection and expansion coefficient determination for signals in a training set, selected to be representative of the signals for which compact representations are desired, using the frame designed in the previous iteration. (2) Update of frame vectors with the objective of improving the representation of step (1). This method for frame design was used by [Engan et al., Signal Processing 80 (2000) 2121-2140] for block-oriented signal expansions, i.e. generalizations of block-oriented transforms and by [Aase et al., IEEE Trans. Signal Process. 49(5) (2001) 1087-1096] for non-block-oriented frames--for short overlapping frames, that may be viewed as generalizations of critically sampled filter banks. Here we give the solution to the general frame design problem using the compact notation of linear algebra. This makes the solution both conceptually and computationally easier, especially for the overlapping frame case. Also, the solution is more general than those presented earlier, facilitating the imposition of constraints, such as symmetry, on the designed frame vectors.