correct_bidirectional_offset.m

function [col_shift,M] = correct_bidirectional_offset(Y,nFrames,us)

% look and correct for phase artifacts due to bi-directional scanning
% with thanks to Fabian Sinz for useful discussions.

if ~exist('us','var'); us = 10; end
if ~exist('nFrames','var'); nFrames = 50; end

if isa(Y,'char')
    Y = read_file(Y,1,nFrames);
elseif isobject(Y);
    details = whos(Y);
    var_sizes = [details.bytes];
    [~,var_ind] = max(var_sizes);
    var_name = details(var_ind).name;
    sizY = size(Y,var_name);
    T = sizY(end);
    if length(sizY) == 3; 
        Y = Y.(var_name)(:,:,1:min(T,nFrames));
    else
        Y = Y.(var_name)(:,:,:,1:min(T,nFrames));
    end
else
    sizY = size(Y); 
    T = sizY(end);
    if ndims(Y) == 3
        Y = Y(:,:,1:min(T,nFrames));
    elseif ndims(Y) == 4
        Y = Y(:,:,:,1:min(T,nFrames));
    end
end

sizY = size(Y);
Y = single(Y);
Y = reshape(Y,[sizY(1:2),prod(sizY(3:end))]);
mY = mean(Y,3);
mY = mY - min(mY(:));
mY1 = mY(1:2:sizY(1)-mod(sizY(1),2),:);
mY2 = mY(2:2:sizY(1),:);

mY1_us = imresize(mY1,[size(mY1,1),size(mY1,2)*us]);
mY2_us = imresize(mY2,[size(mY2,1),size(mY2,2)*us]);

fft1 = fft(mY1_us,[],2);
fft2 = fft(mY2_us,[],2);

buf_prod = fft1.*conj(fft2);

CC = ifft(buf_prod,[],2);
CCabs = abs(CC);
[~,ind] = max(mean(CCabs));
Nc_us = ifftshift(-fix(size(mY1_us,2)/2):ceil(size(mY1_us,2)/2)-1);
col_shift = Nc_us(ind)/us;

if nargout > 1

    Nc = ifftshift(-fix(size(mY1,2)/2):ceil(size(mY1,2)/2)-1);

    min_value = min(Y(:));
    max_value = max(Y(:));
    Y = Y - min_value;  % make data non-negative

    Y1 = Y(1:2:end,:,:);
    Y2 = Y(2:2:end,:,:);
    Ys2 = real(ifft(fft(Y2,[],2).*repmat(exp(-1i*2*pi*col_shift*Nc/sizY(2)),[size(mY2,1),1,prod(sizY(3:end))]),[],2));
    Ys2(:,(1:abs(round(col_shift)))*sign(col_shift) + (sizY(2)+1)*(col_shift<0),:) = Y1(1:end-mod(sizY(1),2),(1:abs(round(col_shift)))*sign(col_shift) + (sizY(2)+1)*(col_shift<0),:);
    clear Y2;
    M = kron(reshape(Y1,size(Y1,1),[]),[1;0]) + kron(reshape(Ys2,size(Ys2,1),[]),[0;1]);
    clear Y1 Ys1;
    if size(M,1) > sizY(1)
        M(sizY(1)+1:end,:) = [];
    end
    M = reshape(M,sizY) + min_value;
    M(M<min_value) = min_value;
    M(M>max_value) = max_value;

end