commGSP/commGSP_reconstruct.m
234a68af8299master

commGSP_reconstruct.m
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			function y = commGSP_reconstruct(A, type, BW, S, x)
			% Reconstructs a graph signal from the provided subsampled version (on
			% a subgraph)
			% INPUT:
			% A - (symmetric) adjacency matrix
			% type - string defining type of the signal to reconstruct:
			% 'smooth', 'non-smooth' (Laplacian-based),
			% 'modular', 'anti-modular' (modularity-based)
			% BW - number of eigenvectors kept in the signal bandwidth
			% S - diagonal matrix defining subgraph on which the signal values
			% are used to reconstruct the signal: entry (i,i) equal
			% to 1 if i^th node belongs to the subgraph, 0 otherwise
			% x - signal to reconstruct (length equal to size of A). Unknown values
			% need to be set to 0.

			% OUTPUT
			% y - reconstructed graph signal

			N=size(A,1);
			if strcmp(type, 'smooth') \|\| strcmp(type, 'non-smooth')
			[U, ~] = commGSP_eig_implicit(A, 'laplacian');
			else
			if strcmp(type, 'modular') \|\| strcmp(type, 'anti-modular')
			[U, ~] = commGSP_eig_implicit(A, 'modularity');
			end
			end

			if strcmp(type, 'smooth') \|\| strcmp(type, 'modular')
			w=1:BW;
			else
			if strcmp(type, 'non-smooth') \|\| strcmp(type, 'anti-modular')
			w=(N-BW+1):N;
			end
			end
			W = sparse(w,w,ones(length(BW),1),N,N);


			B=sparse(UWU');
			[V,PSI] = eigs(sparse(BSB),N); V=sparse(V);
			eigval=diag(sparse(PSI));
			eigval(find(abs(eigval)<1e-9))=0;
			PSI=diag(eigval);

			tmp=diag(PSI.*W); ind=find(tmp~=0);
			rec=sparse(size(tmp,1),size(tmp,2));
			rec(ind)=1./eigval(ind);
			y=Vdiag(rec)V'*x;

			y(find(diag(S)==1))=x(find(diag(S)==1));
			end