Highly Nonlinear Approximations for Sparse Signal Representation
Addapted spline approximation
Download the MATLAB code for this example here.% This example generates a nonuniform spline space adapted to a chirp signal and % constructs a dictionary for sparse approximation of the chirp through refinements of % OOMP and OMP approaches. sp = [ 0 8 ]; L = 2049; x = linspace( sp(1), sp(2), L ); f = cos( 2*pi*x.^2 ); % Generate the chirp on the interval [0 8] partition = FinalProducePartition( sp(1), sp(2), f, 9 ); % Adapted partition nD = CutDic( partition, 4, L, 10 ); % Generate dictionary tol = 0.01*norm(f); [ DS0, Di0, beta0, c0, Q0 ] = OMPFinalRefi( f, nD, tol ); % Refinement for OMP() plot( x, f, x, c0*DS0(:,1:size(beta0,2))' ); % Plot the chirp and the approximation [ DS0, Di0, beta0, c0, Q0 ] = OOMPFinalRefi( f, nD, tol ); % Refinement for OOMP() figure; plot( x, f, x, c0*DS0(:,1:size(beta0,2))' ); % Plot the chirp and the approximation
