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update_temporal_components.m
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update_temporal_components.m
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function [C,f,P,S,YrA] = update_temporal_components(Y,A,b,Cin,fin,P,options)
% update temporal components and background given spatial components
% A variety of different methods can be used and are separated into 2 classes:
% 1-d approaches, where for each component a 1-d trace is computed by removing
% the effect of all the other components and then averaging with the corresponding
% spatial footprint. Then each trace is denoised. This corresponds to a block-coordinate approach
% 4 different 1-d approaches are included, and any custom method
% can be easily incorporated:
% 'project': The trace is projected to satisfy the constraints by the (known) calcium indicator dynamics
% 'constrained_foopsi': The noise constrained deconvolution approach is used. Time constants can be re-estimated (default)
% 'MCEM_foopsi': Alternating between constrained_foopsi and a MH approach for re-estimating the time constants
% 'MCMC': A fully Bayesian method (slowest, but usually most accurate)
% multi-dimensional approaches: (slowest)
% 'noise_constrained':
% C(j,:) = argmin_{c_j} sum(G*c_j),
% subject to: G*c_j >= 0
% ||Y(i,:) - A*C - b*f|| <= sn(i)*sqrt(T)
% The update can happen either in parallel (default) or serial by tuning options.temporal_parallel.
% In the case of parallel implementation the methods 'MCEM_foopsi' and 'noise_constrained' are not supported
% INPUTS:
% Y: raw data ( d X T matrix)
% A: spatial footprints (d x nr matrix)
% b: spatial background (d x 1 vector)
% Cin: current estimate of temporal components (nr X T matrix)
% fin: current estimate of temporal background (1 x T vector)
% P: struct for neuron parameters
% options: struct for algorithm parameters
% LD: Lagrange multipliers (needed only for 'noise_constrained' method).
%
% OUTPUTS:
% C: temporal components (nr X T matrix)
% f: temporal background (1 x T vector)
% P: struct for neuron parameters
% S: deconvolved activity
% Written by:
% Eftychios A. Pnevmatikakis, Simons Foundation, 2015
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 isempty(P) || nargin < 6
active_pixels = find(sum(A,2)); % pixels where the greedy method found activity
unsaturated_pixels = find_unsaturatedPixels(Y); % pixels that do not exhibit saturation
options.pixels = intersect(active_pixels,unsaturated_pixels); % base estimates only on unsaturated, active pixels
end
defoptions = CNMFSetParms;
if nargin < 7 || isempty(options); options = []; end
if ~isfield(options,'deconv_method') || isempty(options.deconv_method); method = defoptions.deconv_method; else method = options.deconv_method; end % choose method
if ~isfield(options,'restimate_g') || isempty(options.restimate_g); restimate_g = defoptions.restimate_g; else restimate_g = options.restimate_g; end % re-estimate time constant (only with constrained foopsi)
if ~isfield(options,'temporal_iter') || isempty(options.temporal_iter); ITER = defoptions.temporal_iter; else ITER = options.temporal_iter; end % number of block-coordinate descent iterations
if ~isfield(options,'bas_nonneg'); options.bas_nonneg = defoptions.bas_nonneg; end
if ~isfield(options,'fudge_factor'); options.fudge_factor = defoptions.fudge_factor; end
if ~isfield(options,'temporal_parallel'); options.temporal_parallel = defoptions.temporal_parallel; end
if ~isfield(options,'full_A') || isempty(options.full_A); full_A = defoptions.full_A; else full_A = options.full_A; end
if isfield(P,'interp'); Y_interp = P.interp; else Y_interp = sparse(d,T); end % missing data
if isfield(P,'unsaturatedPix'); unsaturatedPix = P.unsaturatedPix; else unsaturatedPix = 1:d; end % saturated pixels
mis_data = find(Y_interp); % interpolate any missing data before deconvolution
if ~memmaped && ~isempty(mis_data)
Y(mis_data) = full(Y_interp(mis_data));
end
if (strcmpi(method,'noise_constrained') || strcmpi(method,'project')) && ~isfield(P,'g')
options.flag_g = 1;
if ~isfield(P,'p') || isempty(P.p); P.p = 2; end;
p = P.p;
P = arpfit(Yr,p,options,P.sn);
if ~iscell(P.g)
G = make_G_matrix(T,P.g);
end
else
G = speye(T);
end
K = size(A,2);
if K == 0
C = [];
if exist('fin','var'); f = fin; else f = []; end
S = [];
YrA = [];
P.b = [];
P.c1 = [];
P.neuron_sn = [];
P.gn = [];
return
end
ff = find(sum(A)==0);
if ~isempty(ff)
A(:,ff) = [];
if exist('Cin','var')
if ~isempty(Cin)
Cin(ff,:) = [];
end
end
end
% estimate temporal (and spatial) background if they are not present
if isempty(fin) || nargin < 5 % temporal background missing
bk_pix = (sum(A,2)==0); % pixels with no active neurons
if isempty(b) || nargin < 3
[b,fin] = fast_nmf(double(Y(bk_pix,:)),[],options.nb,50);
% fin = mean(Y(bk_pix,:));
% fin = fin/norm(fin);
b = max(Y*fin',0);
else
fin = max(b(bk_pix,:)'*Y(bk_pix,:),0)/(b(bk_pix,:)'*b(bk_pix,:));
end
end
% construct product A'*Y
AY = mm_fun([A,double(b)],Y);
bY = AY(size(A,2)+1:end,:);
AY = AY(1:size(A,2),:);
AA = sparse(double(A))'*sparse(double(A));
if isempty(Cin) || nargin < 4 % estimate temporal components if missing
Cin = max(AA\double(AY - (A'*b)*fin),0);
ITER = max(ITER,3);
end
if isempty(b) || isempty(fin) || nargin < 5 % re-estimate temporal background
if isempty(b) || nargin < 3
[b,fin] = nnmf(max(Y - A*Cin,0),1);
else
fin = max((b'*Y - (b'*A)*Cin)/norm(b)^2,0);
end
end
if ~memmaped
saturatedPix = setdiff(1:d,unsaturatedPix); % remove any saturated pixels
Ysat = Y(saturatedPix,:);
Asat = A(saturatedPix,:);
bsat = b(saturatedPix,:);
Y = Y(unsaturatedPix,:);
A = A(unsaturatedPix,:);
b = b(unsaturatedPix,:);
d = length(unsaturatedPix);
end
K = size(A,2);
A = [A,double(b)];
S = zeros(size(Cin));
Cin = [Cin;fin];
C = Cin;
if strcmpi(method,'noise_constrained')
Y_res = Y - A*Cin;
mc = min(d,15); % number of constraints to be considered
LD = 10*ones(mc,K);
else
nA = sum(A.^2);
AA = spdiags(nA(:),0,length(nA),length(nA))\(A'*A);
AY = [AY;bY];
AY = double(bsxfun(@times,AY,1./nA(:)));
if strcmpi(method,'constrained_foopsi') || strcmpi(method,'MCEM_foopsi')
P.gn = cell(K,1);
P.b = num2cell(zeros(K,1));
P.c1 = num2cell(zeros(K,1));
P.neuron_sn = num2cell(zeros(K,1));
end
if strcmpi(method,'MCMC')
params.B = 300;
params.Nsamples = 400;
params.p = P.p;
params.bas_nonneg = options.bas_nonneg;
else
params = [];
end
end
p = P.p;
options.p = P.p;
C = double(C);
if options.temporal_parallel
[O,lo] = update_order_greedy(A(:,1:K));
fr = options.fr;
decay_time = options.decay_time;
spk_SNR = options.spk_SNR;
lam_pr = options.lam_pr;
for iter = 1:ITER
for jo = 1:length(O)
%Ytemp = YrA(:,O{jo}(:)) + Cin(O{jo},:)';
%Ytemp = YrA(O{jo}(:),:) + Cin(O{jo},:);
Ytemp = C(O{jo},:) + AY(O{jo}(:),:) - AA(O{jo}(:),:)*C;
Ctemp = zeros(length(O{jo}),T);
Stemp = zeros(length(O{jo}),T);
btemp = zeros(length(O{jo}),1);
sntemp = btemp;
c1temp = btemp;
gtemp = cell(length(O{jo}),1);
if strcmpi(method,'MCMC')
clear samples_mcmc
samples_mcmc(length(O{jo})) = struct();
[samples_mcmc.Cb] = deal(zeros(params.Nsamples,1));
[samples_mcmc.Cin] = deal(zeros(params.Nsamples,1));
[samples_mcmc.sn2] = deal(zeros(params.Nsamples,1));
[samples_mcmc.ns] = deal(zeros(params.Nsamples,1));
[samples_mcmc.ss] = deal(cell(params.Nsamples,1));
[samples_mcmc.ld] = deal(zeros(params.Nsamples,1));
[samples_mcmc.Am] = deal(zeros(params.Nsamples,1));
[samples_mcmc.g] = deal(zeros(params.Nsamples,1));
[samples_mcmc.params] = deal(struct('lam_', [], 'spiketimes_', [], 'A_', [], 'b_', [], 'C_in', [], 'sg', [], 'g', []));
end
parfor jj = 1:length(O{jo})
if p == 0 % p = 0 (no dynamics assumed)
%cc = max(Ytemp(:,jj),0);
cc = max(Ytemp(jj,:),0);
Ctemp(jj,:) = full(cc');
Stemp(jj,:) = Ctemp(jj,:);
else
switch method
case 'project'
cc = plain_foopsi(Ytemp(jj,:),G);
Ctemp(jj,:) = full(cc');
Stemp(jj,:) = Ctemp(jj,:)*G';
case 'constrained_foopsi'
%[cc,cb,c1,gn,sn,spk] = constrained_foopsi(Ytemp(jj,:),[],[],[],[],options);
%gd = max(roots([1,-gn'])); % decay time constant for initial concentration
%gd_vec = gd.^((0:T-1));
if p == 1; model_ar = 'ar1'; elseif p == 2; model_ar = 'ar2'; else error('non supported AR order'); end
spkmin = spk_SNR*GetSn(Ytemp(jj,:));
lam = choose_lambda(exp(-1/(fr*decay_time)),GetSn(Ytemp(jj,:)),lam_pr);
[cc, spk, opts_oasis] = deconvolveCa(Ytemp(jj,:),model_ar,'optimize_b',true,'method','thresholded',...
'optimize_pars',true,'maxIter',10,'smin',spkmin,'window',200,'lambda',lam);
cb = opts_oasis.b;
Ctemp(jj,:) = full(cc(:)' + cb);
Stemp(jj,:) = spk(:)';
Ytemp(jj,:) = Ytemp(jj,:) - Ctemp(jj,:);
btemp(jj) = cb;
c1temp(jj) = 0;
sntemp(jj) = opts_oasis.sn;
gtemp{jj} = opts_oasis.pars(:)';
case 'MCMC'
%SAMPLES = cont_ca_sampler(Ytemp(:,jj),params);
SAMPLES = cont_ca_sampler(Ytemp(jj,:),params);
Ctemp(jj,:) = make_mean_sample(SAMPLES,Ytemp(jj,:));
Stemp(jj,:) = mean(samples_cell2mat(SAMPLES.ss,T));
btemp(jj) = mean(SAMPLES.Cb);
c1temp(jj) = mean(SAMPLES.Cin);
sntemp(jj) = sqrt(mean(SAMPLES.sn2));
gtemp{jj} = mean(exp(-1./SAMPLES.g))';
samples_mcmc(jj) = SAMPLES; % FN added.
end
end
end
C(O{jo}(:),:) = Ctemp;
S(O{jo}(:),:) = Stemp;
if p > 0
if strcmpi(method,'constrained_foopsi') || strcmpi(method,'MCMC');
P.b(O{jo}) = num2cell(btemp);
P.c1(O{jo}) = num2cell(c1temp);
P.neuron_sn(O{jo}) = num2cell(sntemp);
for jj = 1:length(O{jo})
P.gn(O{jo}(jj)) = gtemp(jj);
end
if strcmpi(method,'MCMC');
P.samples_mcmc(O{jo}) = samples_mcmc; % FN added, a useful parameter to have.
end
end
end
fprintf('%i out of %i components updated \n',sum(lo(1:jo)),K);
end
for ii = K + 1:size(C,1)
cc = max(C(ii,:) + AY(ii,:) - AA(ii,:)*C,0);
%cc = full(max(AY(ii,:)+Cin(ii,:),0));
%YrA = YrA - AA(:,ii)*(cc-C(ii,:));
C(ii,:) = cc; %full(cc');
end
%YrA = YrA - AA*(Cin-C);
%YrA = (YA - Cin'*AA)/spdiags(nA(:),0,length(nA),length(nA));
if norm(Cin - C,'fro')/norm(C,'fro') <= 1e-3
% stop if the overall temporal component does not change by much
break;
else
Cin = C;
end
end
else
for iter = 1:ITER
perm = 1:K+size(b,2); randperm(K+size(b,2));
for jj = 1:K
ii = perm(jj);
Ytemp = C(ii,:) + AY(ii,:) - AA(ii,:)*C;
if ii<=K
%ff = find(AA(ii,:));
if P.p == 0 % p = 0 (no dynamics assumed)
%YrA(:,ii) = YrA(:,ii) + Cin(ii,:)';
%Ytemp = YrA(:,ii) + Cin(ii,:)';
cc = max(Ytemp,0);
%YrA(:,ff) = YrA(:,ff) - (cc - C(ii,:)')*AA(ii,ff);
C(ii,:) = full(cc');
S(ii,:) = C(ii,:);
else
switch method
case 'project'
%YrA(:,ii) = YrA(:,ii) + Cin(ii,:)';
%Ytemp = YrA(:,ii) + Cin(ii,:)';
cc = plain_foopsi(Ytemp,G);
%YrA(:,ff) = YrA(:,ff) - (cc - C(ii,:)')*AA(ii,ff);
C(ii,:) = full(cc');
S(ii,:) = C(ii,:)*G';
case 'constrained_foopsi'
%[cc,cb,c1,gn,sn,spk] = constrained_foopsi(Ytemp(jj,:),[],[],[],[],options);
if p == 1; model_ar = 'ar1'; elseif p == 2; model_ar = 'exp2'; else error('non supported AR order'); end
spkmin = options.spk_SNR*GetSn(Ytemp);
lam = choose_lambda(exp(-1/(options.fr*options.decay_time)),GetSn(Ytemp),options.lam_pr);
[cc, spk, opts_oasis] = deconvolveCa(Ytemp,model_ar,'optimize_b',true,'method','thresholded',...
'optimize_pars',true,'maxIter',100,'smin',spkmin,'lambda',lam);
%gd = max(roots([1,-gn'])); % decay time constant for initial concentration
%gd_vec = gd.^((0:T-1));
cb = opts_oasis.b;
C(ii,:) = full(cc(:)' + cb);
S(ii,:) = spk(:)';
P.b{ii} = cb;
P.c1{ii} = 0;
P.neuron_sn{ii} = opts_oasis.sn;
P.gn{ii} = opts_oasis.pars(:)';
case 'MCEM_foopsi'
options.p = length(P.g);
%Ytemp = YrA(:,ii) + Cin(ii,:)';
[cc,cb,c1,gn,sn,spk] = MCEM_foopsi(Ytemp,[],[],P.g,[],options);
gd = max(roots([1,-gn.g(:)']));
gd_vec = gd.^((0:T-1));
%YrA(:,ff) = YrA(:,ff) - (cc(:) + cb + c1*gd_vec' - C(ii,:)')*AA(ii,ff);
C(ii,:) = full(cc(:)' + cb + c1*gd_vec);
S(ii,:) = spk(:)';
P.b{ii} = cb;
P.c1{ii} = c1;
P.neuron_sn{ii} = sn;
P.gn{ii} = gn.g;
case 'MCMC'
params.B = 300;
params.Nsamples = 400;
params.p = P.p; %length(P.g);
%YrA(:,ii) = YrA(:,ii) + Cin(ii,:)';
%Ytemp = YrA(:,ii) + Cin(ii,:)';
SAMPLES = cont_ca_sampler(Ytemp,params);
ctemp = make_mean_sample(SAMPLES,Ytemp);
%YrA(:,ff) = YrA(:,ff) - (ctemp - C(ii,:))'*AA(ii,ff);
C(ii,:) = ctemp';
S(ii,:) = mean(samples_cell2mat(SAMPLES.ss,T));
P.b{ii} = mean(SAMPLES.Cb);
P.c1{ii} = mean(SAMPLES.Cin);
P.neuron_sn{ii} = sqrt(mean(SAMPLES.sn2));
gr = mean(exp(-1./SAMPLES.g));
gp = poly(gr);
P.gn{ii} = -gp(2:end);
P.samples_mcmc(ii) = SAMPLES; % FN added, a useful parameter to have.
case 'noise_constrained'
Y_res = Y_res + A(:,ii)*Cin(ii,:);
[~,srt] = sort(A(:,ii),'descend');
ff = srt(1:mc);
[cc,LD(:,ii)] = lagrangian_foopsi_temporal(Y_res(ff,:),A(ff,ii),T*P.sn(unsaturatedPix(ff)).^2,G,LD(:,ii));
C(ii,:) = full(cc');
Y_res = Y_res - A(:,ii)*cc';
S(ii,:) = C(ii,:)*G';
end
end
else
%YrA(:,ii) = YrA(:,ii) + Cin(ii,:)';
%cc = max(YrA(:,ii),0);
%Ytemp = YrA(:,ii) + Cin(ii,:)';
cc = max(Ytemp,0);
%YrA(:,ii) = YrA(:,ii) - (cc-C(ii,:))'*AA(ii,:);
%YrA = YrA - (cc - C(ii,:)')*AA(ii,:);
C(ii,:) = full(cc');
%YrA(:,ii) = YrA(:,ii) - C(ii,:)';
end
if mod(jj,10) == 0
fprintf('%i out of total %i temporal components updated \n',jj,K);
end
end
if norm(Cin - C,'fro')/norm(C,'fro') <= 1e-3
% stop if the overall temporal component does not change by much
break;
else
Cin = C;
end
end
end
YrA = AY - AA*C;
f = C(K+1:end,:);
C = C(1:K,:);
YrA = YrA(1:K,:);