Normalized Iterative Hard Thresholding for Matrix Completion

2013 ◽  
Vol 35 (5) ◽  
pp. S104-S125 ◽  
Author(s):  
Jared Tanner ◽  
Ke Wei
Keyword(s):  
Matrix Completion ◽  
Hard Thresholding ◽  
Iterative Hard Thresholding

A Sufficient Condition for Low-Rank Recovery via Iterative Hard Thresholding Pursuit

2014 ◽  
Vol 644-650 ◽  
pp. 2378-2381 ◽  
Author(s):  
Li Cui ◽  
Lu Liu ◽  
Xue Zhi Huang
Keyword(s):  
Matrix Completion ◽  
Restricted Isometry Property ◽  
Low Rank ◽  
Performance Guarantee ◽  
Hard Thresholding ◽  
Rank Matrix ◽  
Iterative Hard Thresholding ◽  
Affine Constraints ◽  
Low Rank Matrix ◽  
Matrix Case

In this pape, we propose a matrix Iterative Hard thresholding pursuit algorithm for low-rank minimization that extends Foucart's Hard Thresholding Pursuit (HTP) algorithm from the sparse vector to the low-rank matrix case. The performance guarantee is given in terms of the rank-restricted isometry property and a low-rank solotion is presented. The numerical experiments empirically demonstrate that, although the affine constraints does not satisfy the restricted isometry property in matrix completion, our algorithm also recovers the low-rank matrix from a number of uniformly sampled entries and is more efficient compared with SVT and ADMiRA.

scholarly journals Boundary operation of 2D non-separable oversampled lapped transforms

2016 ◽  
Vol 5 ◽  
Author(s):  
Kosuke Furuya ◽  
Shintaro Hara ◽  
Kenta Seino ◽  
Shogo Muramatsu
Keyword(s):  
Discrete Cosine Transform ◽  
Local Control ◽  
Lattice Structure ◽  
Experimental Results ◽  
Perfect Reconstruction ◽  
Operation Technique ◽  
Two Dimensional ◽  
Hard Thresholding ◽  
Extension Method ◽  
Iterative Hard Thresholding

This paper proposes a boundary operation technique of two-dimensional (2D) non-separable oversampled lapped transforms (NSOLT). The proposed technique is based on a lattice structure consisting of the 2D separable block discrete cosine transform and non-separable redundant support-extension processes. The atoms are allowed to be anisotropic with the oversampled, symmetric, real-valued, compact-supported, and overlapped property. First, the blockwise implementation is developed so that the atoms can be locally controlled. The local control of atoms is shown to maintain perfect reconstruction. This property leads an atom termination (AT) technique as a boundary operation. The technique overcomes the drawback of NSOLT that the popular symmetric extension method is invalid. Through some experimental results with iterative hard thresholding, the significance of AT is verified.

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