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update_spatial_components.m
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update_spatial_components.m
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function [A,b,C,P] = update_spatial_components(Y,C,f,A_,P,options)
% update spatial footprints and background. Two methods are available for
% estimating the components:
% options.spatial_method = 'constrained'
% [A(i,:),b(i)] = argmin sum(A(i,:))
% subject to || Y(i,:) - A(i,:)*C + b(i)*f || <= sn(i)*sqrt(T);
% options.spatial_method = 'regularized'
% [A(i,:),b(i)] = argmin 0.5*|| Y(i,:) - A(i,:)*C + b(i)*f ||^2 + \Lambda^TA(:)
% the support set of each component is determined a-priori
% INPUTS:
% Y: raw data
% C: temporal components
% f: temporal background
% A_: current estimate of spatial footprints (used for determining search locations only)
% P: dataset parameters (used for noise values and interpolated entries)
% options parameter struct (for noise values and other parameters)
% OUTPUTS:
% A: new estimate of spatial footprints
% b: new estimate of spatial background
% C: temporal components (updated only when spatial components are completely removed)
% Written by:
% Eftychios A. Pnevmatikakis, Simons Foundation, 2015
warning('off', 'MATLAB:maxNumCompThreads:Deprecated');
memmaped = isobject(Y);
if memmaped
sizY = size(Y,'Y');
d = prod(sizY(1:end-1));
T = sizY(end);
else
[d,T] = size(Y);
end
if nargin < 6 || isempty(options); options = []; end
if ~isfield(options,'d1') || isempty(options.d1); d1 = input('What is the total number of rows? \n'); options.d1 = d1; else d1 = options.d1; end % # of rows
if ~isfield(options,'d2') || isempty(options.d2); d2 = input('What is the total number of columns? \n'); options.d2 = d2; else d2 = options.d2; end % # of columns
if ~isfield(options,'d3') || isempty(options.d3); d3 = input('What is the total number of z-planes? \n'); options.d3 = d3; else d3 = options.d3; end % # of columns
if ~isfield(options,'interp'); Y_interp = sparse(d,T); else Y_interp = options.interp; end % identify missing data
if ~isfield(options,'spatial_parallel'); spatial_parallel = ~isempty(which('parpool')); else spatial_parallel = options.spatial_parallel; end % use parallel toolbox if present
if ~isfield(options,'search_method'); method = []; else method = options.search_method; end % search method for determining footprint of spatial components
if ~isfield(options,'tsub') || isempty(options.tsub); tsub = 1; else tsub = options.tsub; end % downsample temporally to estimate A and b
if nargin < 2 || (isempty(A_) && isempty(C)) % at least either spatial or temporal components should be provided
error('Not enough input arguments')
else
if ~isempty(C); K = size(C,1); else K = size(A_,2) - options.nb; end
end
if K == 0
A = [];
b = full(A_(:,K+1:end));
C = [];
return
end
if nargin < 5 || isempty(P); P = preprocess_data(Y,1); end % etsimate noise values if not present
if nargin < 4 || isempty(A_)
IND = ones(d,size(C,1));
else
if islogical(A_) % check if search locations have been provided, otherwise estimate them
IND = A_(:,1:K);
if isempty(C)
INDav = double(IND)/diag(sum(double(IND)));
px = (sum(IND,2)>0);
[b,f] = fast_nmf(double(Y(~px,:)),[],options.nb,50);
b = max(Y*f',0)/norm(f)^2;
C = max(INDav'*Y - (INDav'*b)*f,0);
end
if strcmpi(options.spatial_method,'regularized')
A_ = max((Y - b*f)*C'/(C*C'),0);
A_ = A_.*IND;
A_ = [A_,b];
end
else
IND = determine_search_location(A_(:,1:K),method,options);
end
end
K = size(C,1);
if strcmpi(options.spatial_method,'constrained'); A_ = A_(:,1:K); end
Cf = [C;f];
if size(Cf,1) > size(A_,2) && strcmpi(options.spatial_method,'regularized');
error('When using options.spatial_method = regularized pass [A,b] as an input and not just A');
end
if tsub ~= 1 % downsample data
Ts = floor(T/tsub);
Cf_ds = squeeze(mean(reshape(Cf(:,1:Ts*tsub),[],tsub,Ts),2));
T = Ts;
if memmaped
Y_ds = matfile('Y_ds.mat','Writable',true);
Y_ds.Yr(d,T) = double(0);
options.sn = zeros(d,1);
step_size = 2e4;
for i = 1:step_size:d
Ytemp = double(Y.Yr(i:min(i+step_size-1,d),:));
Yt_ds = mean(reshape(Ytemp(:,1:Ts*tsub),[],tsub,Ts),2);
Y_ds.Yr(i:min(i+step_size-1,d),:) = squeeze(Yt_ds);
options.sn(i:min(i+step_size-1,d)) = get_noise_fft(Yt_ds);
end
else
Y_ds = squeeze(mean(reshape(Y(:,1:Ts*tsub),[],tsub,Ts),2));
options.sn = get_noise_fft(Y_ds);
end
else
options.sn = P.sn;
Y_ds = Y;
Cf_ds = Cf;
end
f_ds = Cf_ds(end-size(f,1)+1:end,:);
if strcmpi(options.spatial_method,'constrained')
if spatial_parallel % solve BPDN problem for each pixel
Nthr = max(20*maxNumCompThreads,round(d*T/2^24));
Nthr = min(Nthr,round(d/1e3));
siz_row = [floor(d/Nthr)*ones(Nthr-mod(d,Nthr),1);(floor(d/Nthr)+1)*ones(mod(d,Nthr),1)];
indeces = [0;cumsum(siz_row)];
Yf = cell(Nthr,1);
A = spalloc(d,size(Cf,1),nnz(IND)+size(f,1)*d);
for nthr = 1:Nthr
if memmaped
Ytemp = double(Y_ds.Yr(indeces(nthr)+1:indeces(nthr+1),:));
else
Ytemp = Y_ds(indeces(nthr)+1:indeces(nthr+1),:);
end
sn_temp = options.sn(indeces(nthr)+1:indeces(nthr+1));
IND_temp = IND(indeces(nthr)+1:indeces(nthr+1),:);
Atemp = spalloc(siz_row(nthr),size(Cf,1),nnz(IND_temp));
Yf{nthr} = Ytemp*f_ds';
parfor px = 1:siz_row(nthr)
fn = ~isnan(Ytemp(px,:)); % identify missing data
ind = find(IND_temp(px,:));
if ~isempty(ind);
ind2 = [ind,K+(1:size(f,1))];
[~, ~, a, ~] = lars_regression_noise(Ytemp(px,fn)', Cf_ds(ind2,fn)', 1, sn_temp(px)^2*T);
a_sparse = sparse(1,ind2,double(a'));
Atemp(px,:) = a_sparse';
end
end
if mod(nthr,50) == 0
fprintf('%2.1f%% of pixels completed \n', indeces(nthr+1)*100/d);
end
A(indeces(nthr)+1:indeces(nthr+1),:) = Atemp;
end
Yf = cell2mat(Yf);
else
A = [zeros(d,K),zeros(d,size(f,1))];
sA = zeros(d1,d2,d3);
Yf = Y_ds*f_ds';
for px = 1:d % estimate spatial components
fn = ~isnan(Y_ds(px,:)); % identify missing data
ind = find(IND(px,:));
if ~isempty(ind);
ind2 = [ind,K+(1:size(f,1))];
[~, ~, a, ~] = lars_regression_noise(Y_ds(px,fn)', Cf_ds(ind2,fn)', 1, options.sn(px)^2*T);
A(px,ind2) = a';
sA(px) = sum(a);
end
end
end
elseif strcmpi(options.spatial_method,'regularized')
options.nb = size(f,1);
A = update_spatial_lasso(Y_ds, A_, Cf_ds, IND, options.sn, [], [], options);
K = size(A,2)-options.nb;
b = full(A(:,K+1:end));
A = A(:,1:K);
C = C(1:K,:);
end
A(isnan(A))=0;
A = sparse(double(A));
A = threshold_components(A,options); % post-processing of components
fprintf('Updated spatial components \n');
ff = find(sum(A(:,1:K))==0); % remove empty components
if ~isempty(ff)
K = K - length(ff);
A(:,ff) = [];
C(ff,:) = [];
Cf_ds(ff,:) = [];
end
if memmaped; delete('Y_ds.mat'); end
if strcmpi(options.spatial_method,'constrained');
b = double(max((double(Yf) - A(:,1:K)*double(Cf_ds(1:K,:)*f_ds'))/(f_ds*f_ds'),0));
A = A(:,1:K);
end