Algorithm 2. The Matlab code for training multiple ANN system

% $X^{\prime }$- input matrix 96 × 50000 of training cases

% $Y^{\prime }$- output matrix 2883 × 50000 of training cases

% Choose a Training Function

trainFcn = 'trainlm'; % In this case Levenberg-Marquardt backpropagation was chosen

hiddenLayerSize = 10;  % Choose a number of hidden layers

net = fitnet(hiddenLayerSize,trainFcn);  % Create a fitting network under variable ‘net’

% Choose input and output pre/post-processing functions

% ‘removeconstantrows’ - remove matrix rows with constant values

% ‘mapminmax’ - map matrix row minimum and maximum values to [−1 1]

net.input.processFcns = {'removeconstantrows','mapminmax'};

net.output.processFcns = {'removeconstantrows','mapminmax'};

% Setup division of data for training, validation, testing

net.divideFcn = 'dividerand'; % Divide data randomly

net.divideMode = 'sample'; % Divide up every sample

net.divideParam.trainRatio = 70/100; % 70% of cases is allocated for training

net.divideParam.valRatio = 15/100; % 15% of cases is allocated for validation

net.divideParam.testRatio = 15/100; % 15% of cases is allocated for testing

net.performFcn = 'mse'; % Mean Squared Error will be used for performance evaluation

x = X';

y = Y';

N=2883; % The resolution of output picture grid

parfor i=1:N  % Start ‘for’ loop with parallel computing

% Assign an i-th row of reference cases to the variable t. Each of the 2883 lines corresponds

% to one pixel of the output image

t = y(i,:);

% Train the network. The variable ‘nets_for_pixels’ is a structure that consists of 2883

% separately trained neural networks.

[nets_for_pixels{i},~] = train(net,x,t);

end % End ‘parfor’ loop