daniele@179: function mu = cumcoherence(obj,p)
daniele@179: % Calculates the p-cumulative coherence of the dictionary, defined as
daniele@179: % \mu_p(k) = max_|I|=k{max_j\notin I{(\sum_i \in I}|<\phi_i,\phi_j>|^p)^1/p}
daniele@179: %
daniele@179: % INPUT
daniele@179: % obj: dictionary object
daniele@179: % p: power (default 1)
daniele@179: %
daniele@179: % OUTPUT
daniele@179: % mu: p-cumulative coherence
daniele@180: if ~exist('p','var') || isempty(p), p = 1; end
daniele@179: 
daniele@160: obj = normalize(obj);
daniele@160: [M N] = size(obj.phi);
daniele@160: mu = zeros(M,1);
daniele@160: for m=1:M
daniele@179: 	c = zeros(N);
daniele@179: 	for i=1:N
daniele@179: 		c(:,i) = abs(obj.phi'*obj.phi(:,i)).^p;
daniele@179: 		c(i,i) = 0;
daniele@179: 	end
daniele@179: 	c = sort(c,'descend');
daniele@179: 	c = c(1:m,:);
daniele@179: 	if m==1
daniele@180: 		mu(m) = max(c.^(1/p));
daniele@179: 	else
daniele@180: 		mu(m) = max(sum(c).^(1/p));
daniele@179: 	end
daniele@160: end
daniele@160: end