scholarly journals Denoising strategies for general finite frames

2018 ◽  
Vol 147 ◽  
pp. 90-99
Author(s):  
D. De Canditiis ◽  
M. Pensky ◽  
P.J. Wolfe
Keyword(s):  
Finite Frames

scholarly journals On structural decompositions of finite frames

2015 ◽  
Vol 42 (3) ◽  
pp. 721-756
Author(s):  
Alice Z.-Y. Chan ◽  
Martin S. Copenhaver ◽  
Sivaram K. Narayan ◽  
Logan Stokols ◽  
Allison Theobold
Keyword(s):  
Finite Frames ◽  
Structural Decompositions

Algebraic Geometry and Finite Frames

Finite Frames ◽  
2013 ◽  
pp. 141-170 ◽  
Author(s):  
Jameson Cahill ◽  
Nate Strawn
Keyword(s):  
Algebraic Geometry ◽  
Finite Frames

Spanning and Independence Properties of Finite Frames

Finite Frames ◽  
2013 ◽  
pp. 109-139
Author(s):  
Peter G. Casazza ◽  
Darrin Speegle
Keyword(s):  
Finite Frames ◽  
Independence Properties

Parseval transforms for finite frames

2018 ◽  
Vol 16 (03) ◽  
pp. 1850014 ◽  
Author(s):  
Xianwei Zheng ◽  
Shouzhi Yang ◽  
Yuan Yan Tang ◽  
Youfa Li
Keyword(s):  
Frame Theory ◽  
Square Root ◽  
Graph Structure ◽  
Finite Frames ◽  
Frame Operator ◽  
Finite Frame ◽  
Parseval Frames ◽  
Schmidt Orthogonalization ◽  
The Right ◽  
The Relationship

The relationship between frames and Parseval frames is an important topic in frame theory. In this paper, we investigate Parseval transforms, which are linear transforms turning general finite frames into Parseval frames. We introduce two classes of transforms in terms of the right regular and left Parseval transform matrices (RRPTMs and LPTMs). We give representations of all the RRPTMs and LPTMs of any finite frame. Two important LPTMs are discussed in this paper, the canonical LPTM (square root of the inverse frame operator) and the RGS matrix, which are obtained by using row’s Gram–Schmidt orthogonalization. We also investigate the relationship between the Parseval frames generated by these two LPTMs. Meanwhile, for RRPTMs, we verify the existence of invertible RRPTMs for any given finite frame. Finally, we discuss the existence of block diagonal RRPTMs by taking the graph structure of the frame elements into consideration.

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