Question about noise covariance

matthewpesce22 · April 13, 2020, 3:33pm

Hello,

I was looking through the tutorial on noise covariance and came across this option for calculating the matrix for epilepsy data.

Option #1a Compute the noise covariance statistics from blocks of recordings away from the peak of any identified interictal spike, and keep only the diagonal (the variance of the sensors).

I was wondering if by 'keep only the diagonal' it was meant to export the files to matlab and zero all other values? If so, would you zero the non-diagonal values from the NoiseCov variable as well as the FourthMoment?

I apologize if this has gone under the wrong Topic

-Matthew

Francois · April 15, 2020, 8:42am

This indication 'keep only the diagonal' is described in the previous options in the same section. As it was not obvious, I copied the text from the EEG resting state section in the epilepsy section:

This option is available in Brainstorm's advanced options of source computation: select the option "Diagonal noise covariance".

You don't need to modify the noise covariance file explicitly, this is done automatically during the estimation of the sources. When the option "Diagonal noise covariance" is selected, NoiseMethod='diag' in the source estimation function, bst_inverse_linear_2018.m, and in this case, the variable 'FourthMoment' is not used at all:

github.com

brainstorm-tools/brainstorm3/blob/master/toolbox/inverse/bst_inverse_linear_2018.m#L249


      
          nChannels = length(Var_noise);
          
          % JCM: March 2015, probably don't need this, but will retain
          % Detect if the input noise covariance matrix is or should be diagonal
          if (norm(C_noise,'fro') - norm(Var_noise,'fro')) < eps(single(norm(Var_noise,'fro')))
              % no difference between the full matrix and the diagonal matrix
              disp(['BST_INVERSE > Detected diagonal noise covariance, enforcing option NoiseMethod="' OPTIONS.NoiseMethod '".']);
              OPTIONS.NoiseMethod = 'diag';
          end
          
          if strcmpi('diag',OPTIONS.NoiseMethod)
              C_noise = diag(diag(C_noise)); % force matrix to be diagonal, that's all the user wants
          end
          
          % Commentary April 2015: There is a tendency to apply generic scale values to the
          % channels to balance them with regards to units, such as Volts and Tesla.
          % But we also have a problem with gradiometer channels vs magnetometers. So
          % the "natural" way is to use the channel variances themselves to balance
          % out the differences between modalities. But we don't want to do each
          % channel, since a dead channel has (near) zero variance. So instead we
          % calculate a common variance for each modality, to get us in the ball

github.com

brainstorm-tools/brainstorm3/blob/master/toolbox/inverse/bst_inverse_linear_2018.m#L1157


      
              
          case 'median'
              if VERBOSE
                  fprintf('BST_INVERSE > Covariance regularized by flattening tail of eigenvalues spectrum to the median value of %.1e\n',median(Sn));
              end
              Sn = max(Sn,median(Sn)); % removes deficient small values
              Cov = Un*diag(Sn.^2)*Un'; % rebuild again.
              iW = Un*diag(1./Sn)*Un'; % inverse whitener
              
          case 'diag'
              Cov = diag(diag(Cov)); % strip to diagonal
              iW = diag(1./sqrt(diag(Cov))); % inverse of diagonal
              if VERBOSE
                  fprintf('BST_INVERSE > Covariance matrix reduced to diagonal.\n');
              end
              
          case 'reg'
              % The unit of "Regularize Noise Covariance" is as a percentage of
              % the mean variance of the modality.
                      
              % Ridge Regression: