NDLI: Homotopy algorithm for l 1-norm minimisation problems

Please wait, while we are loading the content...

Effect of polynomial interpolations on the estimation performance of a frequency-selective Rayleigh channel in orthogonal frequency division multiplexing systems

Electrocardiogram signal denoising using non-local wavelet transform domain filtering

Enhanced distributed estimation based on prior information

Estimation of Teager energy using the Hilbert–Huang transform

Finite-state entropy-constrained vector quantiser for audio modified discrete cosine transform coefficients uniform quantisation

Homotopy algorithm for l 1-norm minimisation problems

Joint detection, tracking and classification of a manoeuvring target in the finite set statistics framework

Modelling and forecasting of signal-to-interference plus noise ratio in femtocellular networks using logistic smooth threshold autoregressive model

Non-myopic sensor scheduling to track multiple reactive targets

Widely-linear minimum-mean-squared error multiple-candidate successive interference cancellation for multiple access interference and jamming suppression in direct-sequence code-division multiple-access systems

IET Wireless Sensor Systems

Micro & Nano Letters

The Journal of Engineering

Homotopy algorithm for l 1-norm minimisation problems

Content Provider	IET Digital Library
Author	Dai, Jisheng Xu, Weichao Zhang, Jin Chang, Chunqi
Abstract	This paper proposes a novel approach to handle the singularity problem in the Homotopy algorithm. Following a state-of-art ridge-adding-based method, the authors introduce a random ridge term to each element of the measure matrix to avoid the occurrence of singularities. Then, the authors give the sufficient condition of avoiding singularities, and prove that adding random ridge is greatly useful to deal with the singularity problem, even the random ridge tends to zero. Although the main procedures in the method coincide with the state-of-art method, all the derivations and theoretical analyses are different because of distinct forms of optimisation problems. Thus, this work is by no means a trivial task. Moreover, the authors note that the most computationally expensive step in the proposed method is the inversion of active matrices, whose time complexity relative to that of other required operations is proportional to the active set's cardinality. This motivates us to develop an efficient QR update algorithm based on the new ridge-adding-based method, which is incorporated in Givens QR factorisation and Gaussian elimination. It turns out that, with such new QR update algorithm, the previous ratio of time complexities can be reduced to a constant order. As a consequence, the new method can eliminate the bottleneck of matrix inversion in the improved Homotopy algorithm.
Starting Page	1
Ending Page	9
Page Count	9
ISSN	17519675
Volume Number	9
e-ISSN	17519683
Issue Number	Issue 1, Feb (2015)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/9/1
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2013.0338
Journal	IET Signal Processing
Publisher	The Institution of Engineering and Technology
Publisher Date	2015-02-23
Access Restriction	Open
Rights License	Creative Commons Attribution-Non Commercial License (http://creativecommons.org/licenses/by-nc/3.0/)
Subject Keyword	Active Matrices Algebra Gaussian Elimination Gaussian Processes Homotopy Algorithm L1-norm Minimisation Problem Matrix Algebra Matrix Inversion Matrix Measurement Minimisation Optimisation Optimisation Problem Optimisation Technique Ridge Adding Based Method Singularity Problem State-of-art Ridge Adding Based Method Statistics
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

Block-sparse signal recovery based on truncated ℓ1 minimisation in non-Gaussian noise

FLRR: fast low-rank representation using Frobenius-norm

Reweighted l1-norm minimisation for high-resolution DOA estimation under unknown mutual coupling

Simple algorithm for L1-norm regularisation-based compressed sensing and image restoration

L1-norm based discriminant manifold learning for multi-label image classification

A reduced l 2–l 1 model with an alternating minimisation algorithm for support recovery of multiple measurement vectors

Efficient method for finding globally optimal solution of problem with weighted Lp norm and L 2 norm objective function

Designing sequence sets with good correlation properties based on PSD fitting

Kullback–Leibler divergence for interacting multiple model estimation with random matrices

Homotopy algorithm for l 1-norm minimisation problems

Similar Documents

Block-sparse signal recovery based on truncated ℓ1 minimisation in non-Gaussian noise

FLRR: fast low-rank representation using Frobenius-norm

Reweighted l1-norm minimisation for high-resolution DOA estimation under unknown mutual coupling

Simple algorithm for L1-norm regularisation-based compressed sensing and image restoration

L1-norm based discriminant manifold learning for multi-label image classification

A reduced l 2–l 1 model with an alternating minimisation algorithm for support recovery of multiple measurement vectors

Efficient method for finding globally optimal solution of problem with weighted Lp norm and L 2 norm objective function

Designing sequence sets with good correlation properties based on PSD fitting

Kullback–Leibler divergence for interacting multiple model estimation with random matrices

Homotopy algorithm for l 1-norm minimisation problems