Download presentation

Presentation is loading. Please wait.

Published byNayeli Tock Modified over 2 years ago

1
**L1-magic : Recovery of Sparse Signals via Convex programming by 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 Peyré CNRS, CEREMADE, Université Paris Dauphine. Justin Romberg School of Electrical and Computer Engineering Georgia Tech

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

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

Similar presentations

OK

What is Mental Health The term mental health is used to describe cognitive and emotional well being with respect to all mental faculties and state.

What is Mental Health The term mental health is used to describe cognitive and emotional well being with respect to all mental faculties and state.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on first conditional questions Ppt on surface area and volume of cylinder and cone Ppt on depreciation of indian rupee 2013 Ppt on albert einstein at school Ppt on thermal conductivity of insulating powders Ppt on oil circuit breaker Ppt on reaction mechanism in organic chemistry Ppt on rhs congruence Ppt on web portal project Imod display ppt online