Denoising by sparse approximation: error bounds based on rate-distortion theory
EURASIP Journal on Applied Signal Processing
Sparse representations are most likely to be the sparsest possible
EURASIP Journal on Applied Signal Processing
Foundations and Trends in Signal Processing
New algorithms for designing unimodular sequences with good correlation properties
IEEE Transactions on Signal Processing
Designing unimodular sequence sets with good correlations: including an application to MIMO radar
IEEE Transactions on Signal Processing
Parametric dictionary design for sparse coding
IEEE Transactions on Signal Processing
Constructions of equiangular tight frames with genetic algorithms
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Non-negative sparse modeling of textures
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
MIMO radar waveform design via alternating projection
IEEE Transactions on Signal Processing
Waveform design for MIMO radar using an alternating projection approach
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Optimized projection matrix for compressive sensing
EURASIP Journal on Advances in Signal Processing
Maximum likelihood estimation of DOD and DOA for bistatic MIMO radar
Signal Processing
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Tight frames, also known as general Welch-bound- equality sequences, generalize orthonormal systems. Numerous applications - including communications, coding, and sparse approximation- require finite-dimensional tight frames that possess additional structural properties. This paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems (IEPs), which includes the frame design problem. To apply this method, one needs only to solve a matrix nearness problem that arises naturally from the design specifications. Therefore, it is the fast and easy to develop versions of the algorithm that target new design problems. Alternating projection will often succeed even if algebraic constructions are unavailable. To demonstrate that alternating projection is an effective tool for frame design, the paper studies some important structural properties in detail. First, it addresses the most basic design problem: constructing tight frames with prescribed vector norms. Then, it discusses equiangular tight frames, which are natural dictionaries for sparse approximation. Finally, it examines tight frames whose individual vectors have low peak-to-average-power ratio (PAR), which is a valuable property for code-division multiple-access (CDMA) applications. Numerical experiments show that the proposed algorithm succeeds in each of these three cases. The appendices investigate the convergence properties of the algorithm.