comparison toolboxes/AudioInpaintingToolbox/Solvers/inpaintFrame_OMP_Gabor.m @ 138:56d719a5fd31 ivand_dev

Audio Inpaintin Toolbox

+function [y , Coeff]= inpaintFrame_OMP_Gabor(problemData,param)
+% Inpainting method based on OMP using the Gabor dictionary
+% generated by Gabor_Dictionary.m. The method jointly selects
+% cosine and sine atoms at the same frequency
+%
+% Usage: y = inpaintFrame_OMP_Gabor(problemData,param)
+%
+%
+% Inputs:
+%          - problemData.x: observed signal to be inpainted
+%          - problemData.Imiss: Indices of clean samples
+%          - param.D - the dictionary matrix (optional if param.D_fun is set)
+%          - param.D_fun - a function handle that generates the dictionary 
+%          matrix param.D if param.D is not given. See Gabor_Dictionary.m
+%          - param.wa - Analysis window
+%
+% Outputs:
+%          - y: estimated frame
+%
+%
+% -------------------
+%
+% Audio Inpainting toolbox
+% Date: June 28, 2011
+% By Valentin Emiya, Amir Adler, Michael Elad, Maria Jafari
+% This code is distributed under the terms of the GNU Public License version 3 (http://www.gnu.org/licenses/gpl.txt).
+% ========================================================
+% To do next: use a faster implementation of OMP
+
+
+%% Load data and parameters
+
+
+x = problemData.x;
+IObs = find(~problemData.IMiss);
+p.N = length(x);
+E2 = param.OMPerr^2;
+E2M=E2*length(IObs);
+wa = param.wa(param.N);
+
+%% Build and normalized dictionary
+% build the dictionary matrix if only the dictionary generation function is given
+if ~isfield(param,'D')
+    param.D = param.D_fun(param);
+end
+Dict=param.D(IObs,:);
+W=1./sqrt(diag(Dict'*Dict));
+Dict=Dict*diag(W);
+Dict1 = Dict(:,1:end/2);
+Dict2 = Dict(:,end/2+1:end);
+Dict1Dict2 = sum(Dict1.*Dict2);
+n12 = 1./(1-Dict1Dict2.^2);
+xObs=x(IObs);
+
+%% OMP iterations
+residual=xObs;
+maxNumCoef = param.sparsityDegree;
+indx = [];
+% currResNorm2 = sum(residual.^2);
+currResNorm2 = E2M*2; % set a value above the threshold in order to have/force at least one loop executed
+j = 0;
+while currResNorm2>E2M && j < maxNumCoef,
+    j = j+1;
+    proj=residual'*Dict;
+    proj1 = proj(1:end/2);
+    proj2 = proj(end/2+1:end);
+    
+    alpha_j = (proj1-Dict1Dict2.*proj2).*n12;
+    beta_j = (proj2-Dict1Dict2.*proj1).*n12;
+    
+    err_j = sum(abs(repmat(residual,1,size(Dict1,2))-Dict1*sparse(diag(alpha_j))-Dict2*sparse(diag(beta_j))).^2);
+    [dum pos] = min(err_j);
+    
+    indx(end+1)=pos;
+    indx(end+1)=pos+size(Dict1,2);
+    a=pinv(Dict(:,indx(1:2*j)))*xObs;
+    residual=xObs-Dict(:,indx(1:2*j))*a;
+    currResNorm2=sum(residual.^2);
+end;
+
+%% Frame Reconstruction
+indx(length(a)+1:end) = [];
+
+Coeff = sparse(size(param.D,2),1);
+if (~isempty(indx))
+    Coeff(indx) = a;
+    Coeff = W.*Coeff;
+end
+y = param.D*Coeff;
+
+return
+
+