Notes:

To determine the contribution (or amount of “explanation”) the 2nd singular value and it’s associated temporal and spatial modes make, The second diagonal element of S is left intact and all remaining diagonal elements (associated with the other singular values) are set to zero.

This then determines (via matrix multiplication properties) which elements of T and E contribute to regenerating the original image series, P.

Selecting the 2nd singular value means only the 2nd column of T, and the 2nd column of ET are used in determining the contribution from the 2nd singular value.

In this example, it is clear from the resulting matrix P’ that the 2nd singular value (and it’s associated spatial mode) account for none of the voxel values in the 1st image, and all of the voxel values in the 2nd image.