Approximation by structured lower rank matrices

Moody T. Chu; Robert E. Funderlic; Robert J. Plemmons

doi:10.1117/12.325687

2 October 1998 Approximation by structured lower rank matrices

Moody T. Chu, Robert E. Funderlic, Robert J. Plemmons

Proceedings Volume 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII; (1998) https://doi.org/10.1117/12.325687
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

We consider two general procedures for constructing the nearest approximation of a given matrix by one with any lower rank and any linear structure. Nearness can be measured in any matrix norm. Structured low rank matrices arise in various applications, including image enhancement and model reduction. In practice, the empirical data collected in the matrix often either do not maintain the specified structure or do not induce the desirable rank.It is an important task to search for the nearest structured lower rank approximation of a given matrix. The techniques developed in this paper can easily be implemented for numerical computation. In particular, it is shown that the computations can be approached using efficient optimization packages. The special case of Toeplitz structure using the Frobenius matrix norm is discussed in detail to illustrate the ideas, and numerical test are reported. The procedures developed herein can be generalized to consider a much broader range of approximation problems.

Citation Download Citation

Moody T. Chu, Robert E. Funderlic, and Robert J. Plemmons "Approximation by structured lower rank matrices", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); https://doi.org/10.1117/12.325687

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