1 / 5

L1-magic : Recovery of Sparse Signals via Convex programming by Emmanuel Cand è s and Justin Romberg

L1-magic : Recovery of Sparse Signals via Convex programming by Emmanuel Cand è s and Justin Romberg. Caltech October 2005 Compressive Sensing Tutorial PART 2 Svetlana Avramov-Zamurovic January 22, 2009. Definitions. X desired vector (N elements), K sparse Y measurements (M elements), K<M<N

silas
Download Presentation

L1-magic : Recovery of Sparse Signals via Convex programming by Emmanuel Cand è s and Justin Romberg

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. L1-magic : Recovery of Sparse Signals via Convex programmingby Emmanuel Candès and Justin Romberg Caltech October 2005 Compressive Sensing Tutorial PART 2 Svetlana Avramov-Zamurovic January 22, 2009.

  2. Definitions • X desired vector (N elements), K sparse • Y measurements (M elements), K<M<N • Ψ orthonormal basis (NxN), X= Ψs • Φ measurement matrix (MxN) • L1 norm= sum(abs(all vector X elements)) • Linear programming • Find sparse solution that satisfies measurements, Y= ΦX and minimizes the L1 norm of X

  3. MATLAB programs http://sparselab.stanford.edu/ Gabriel PeyréCNRS, CEREMADE, Université Paris Dauphine. http://www.ceremade.dauphine.fr/~peyre/ Justin RombergSchool of Electrical and Computer EngineeringGeorgia Tech http://users.ece.gatech.edu/~justin/Justin_Romberg.html

  4. Min-L1 with equality constraints When x, A, b have real-valued entries, (P1) can be recast as an LP. % load random states for repeatable experiments rand_state=1;randn_state=1;rand('state', rand_state);randn('state', randn_state); N = 512;% signal length T = 20;% number of spikes in the signal K = 120;% number of observations to make x = zeros(N,1);q = randperm(N);x(q(1:T)) = sign(randn(T,1)); % random +/- 1 signal% %SAZ original signal to be recovered disp('Creating measurment matrix...');A = randn(K,N);A = orth(A')';disp('Done.'); y = A*x;% observations SAZ measurements x0 = A'*y;% initial guess = min energy xp = l1eq_pd(x0, A, [], y, 1e-3); % solve the LP http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

  5. N=512 K=20 M=120 N=512 K=20 M=80

More Related