NDLI: Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries

Content Provider	IET Digital Library
Author	Prater, Ashley Shen, Lixin
Abstract	In many applications, one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampled set of linear projections of the composite signal. In this study, the authors propose using the Dantzig selector model incorporating an overcomplete dictionary to separate a noisy undersampled collection of composite signals, and present an algorithm to efficiently solve the model. The Dantzig selector is a statistical approach to finding a solution to a noisy linear regression problem by minimising the ℓ1 norm of candidate coefficient vectors while constraining the scope of the residuals. The Dantzig selector performs well in the recovery and separation of an unknown composite signal when the underlying coefficient vector is sparse. They propose a proximity operator-based algorithm to recover and separate unknown noisy undersampled composite signals using the Dantzig selector. They present numerical simulations comparing the proposed algorithm with the competing alternating direction method, and the proposed algorithm is found to be faster, while producing similar quality results. In addition, they demonstrate the utility of the proposed algorithm by applying it in various applications including the recovery of complex-valued coefficient vectors, the removal of impulse noise from smooth signals, and the separation and classification of a composition of handwritten digits.
Starting Page	226
Ending Page	234
Page Count	9
ISSN	17519675
Volume Number	9
e-ISSN	17519683
Issue Number	Issue 3, May (2015)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/9/3
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2014.0048
Journal	IET Signal Processing
Publisher Date	2015-04-17
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Alternating Direction Method Complex-valued Coefficient Vector Compressed Sensing Compressive Sensing Framework Dantzig Selector Handwritten Digits Impulse Noise Linear Projections Noisy Linear Regression Problem Numerical Analysis Numerical Method Numerical Simulation Overcomplete Dictionaries Overcomplete Dictionary Proximity Operator Regression Analysis Signal Processing And Detection Signal Processing Theory Smooth Signal Smoothing Method Source Separation Statistical Approach Statistics Undersampled Collection Undersampled Composite Signal Separation
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

Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries

Dictionaries Construction Using Alternating Projection Method in Compressive Sensing

A new algorithm for learning overcomplete dictionaries

The Linearized Alternating Direction Method of Multipliers for Dantzig Selector

Dantzig selector for audio data reconstruction

Single image super-resolution using compressive sensing with learned overcomplete dictionary

Compressive sensing ultrasound imaging using overcomplete dictionaries

Compressive Sensing of Neural Action Potentials by Designing Overcomplete Dictionaries

Adaptive compressed sensing of speech signal based on data-driven dictionary

Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries

Similar Documents

Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries

Dictionaries Construction Using Alternating Projection Method in Compressive Sensing

A new algorithm for learning overcomplete dictionaries

The Linearized Alternating Direction Method of Multipliers for Dantzig Selector

Dantzig selector for audio data reconstruction

Single image super-resolution using compressive sensing with learned overcomplete dictionary

Compressive sensing ultrasound imaging using overcomplete dictionaries

Compressive Sensing of Neural Action Potentials by Designing Overcomplete Dictionaries

Adaptive compressed sensing of speech signal based on data-driven dictionary

Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries