Perturbation analysis of signal space fast iterative hard thresholding with redundant dictionaries

2017 ◽  
Vol 11 (4) ◽  
pp. 462-468 ◽  
Author(s):  
Haifeng Li ◽  
Guoqi Liu
Keyword(s):  
Perturbation Analysis ◽  
Hard Thresholding ◽  
Signal Space ◽  
Iterative Hard Thresholding ◽  
Redundant Dictionaries

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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