Fast Singular Value Shrinkage with Chebyshev Polynomial Approximation Based on Signal Sparsity

May 19, 2017 ยท Declared Dead ยท ๐Ÿ› IEEE Transactions on Signal Processing

๐Ÿ‘ป CAUSE OF DEATH: Ghosted
No code link whatsoever

"No code URL or promise found in abstract"

Evidence collected by the PWNC Scanner

Authors Masaki Onuki, Shunsuke Ono, Keiichiro Shirai, Yuichi Tanaka arXiv ID 1705.07112 Category math.NA: Numerical Analysis Cross-listed cs.LG Citations 10 Venue IEEE Transactions on Signal Processing Last Checked 1 month ago
Abstract
We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the rank of a given data matrix with other cost functions and/or constraints, which is called matrix rank minimization. In matrix rank minimization, singular values of a matrix are shrunk by hard-thresholding, soft-thresholding, or weighted soft-thresholding. However, the computational cost of SVD is generally too expensive to handle high dimensional signals such as images; hence, in this case, matrix rank minimization requires enormous computation time. In this paper, we leverage CPA to (approximately) manipulate singular values without computing singular values and vectors. The thresholding of singular values is expressed by a multiplication of certain matrices, which is derived from a characteristic of CPA. The multiplication is also efficiently computed using the sparsity of signals. As a result, the computational cost is significantly reduced. Experimental results suggest the effectiveness of our method through several image processing applications based on matrix rank minimization with nuclear norm relaxation in terms of computation time and approximation precision.
Community shame:
Not yet rated
Community Contributions

Found the code? Know the venue? Think something is wrong? Let us know!

๐Ÿ“œ Similar Papers

In the same crypt โ€” Numerical Analysis

R.I.P. ๐Ÿ‘ป Ghosted

Tensor Ring Decomposition

Qibin Zhao, Guoxu Zhou, ... (+3 more)

math.NA ๐Ÿ› arXiv ๐Ÿ“š 427 cites 9 years ago

Died the same way โ€” ๐Ÿ‘ป Ghosted