NDLI: Optimal design of orders of DFrFTs for sparse representations

Content Provider	IET Digital Library
Author	Zhang, Xiao Zhi Ling, Bingo Wing Kuen Tao, Ran Yang, Zhi Jing Woo, Wai Lok Sanei, Saeid Teo, Kok L.
Abstract	This study proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimisation problem with an L 1 -norm non-convex objective function. To avoid all the orders of the DFrFTs to be the same, the exclusive OR of two constraints are imposed. The constrained optimisation problem is further reformulated to an optimal frequency sampling problem. A method based on solving the roots of a set of harmonic functions is employed for finding the optimal sampling frequencies. As the designed overcomplete transform can exploit the physical meanings of the signals in terms of representing the signals as the sums of the components in the time–frequency plane, the designed overcomplete transform can be applied to many applications.
Starting Page	1023
Ending Page	1033
Page Count	11
ISSN	17519675
Volume Number	12
e-ISSN	17519683
Issue Number	Issue 8, Oct (2018)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/12/8
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2017.0283
Journal	IET Signal Processing
Publisher Date	2018-04-27
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Concave Programming Constrained Optimisation Problem DFrFT Orders Digital Signal Processing Discrete Fourier Transform Discrete Fractional Fourier Transforms Harmonic Function Integral Transforms L1-norm Nonconvex Objective Function Optimal Design Optimal Frequency Sampling Problem Optimisation Technique Overcomplete Transform Signal Processing And Detection Signal Representation Signal Sampling Sparse Representations Time-frequency Plane
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms

Optimal design of orders of discrete fractional Fourier transforms for sparse representations

Direct Batch Evaluation of Optimal Orthonormal Eigenvectors of the DFT Matrix

Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices

Sparse signal recovery via minimax-concave penalty and ℓ1-norm loss function

The multiple-parameter discrete fractional Fourier transform

Sparse Discrete Fractional Fourier Transform and Its Applications

On the multiangle centered discrete fractional Fourier transform

A digital watermarking algorithm based on hyperchaos and discrete fractional Fourier transform

Optimal design of orders of DFrFTs for sparse representations

Similar Documents

Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms

Optimal design of orders of discrete fractional Fourier transforms for sparse representations

Direct Batch Evaluation of Optimal Orthonormal Eigenvectors of the DFT Matrix

Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices

Sparse signal recovery via minimax-concave penalty and ℓ1-norm loss function

The multiple-parameter discrete fractional Fourier transform

Sparse Discrete Fractional Fourier Transform and Its Applications

On the multiangle centered discrete fractional Fourier transform

A digital watermarking algorithm based on hyperchaos and discrete fractional Fourier transform

Optimal design of orders of DFrFTs for sparse representations