Hi Jian,

The change of basis you need to perform depends on the basis you use for the measurements, so only you can know.

If you use a Hadamard basis, then you need to multiply by the inverse of the Hadamard matrix (which is conveniently a Hadamard matrix) to retrieve the matrix in the pixel basis.

What you measure is T' = T \times Ha with Ha the Hadamard matrix and T the transmission matrix.

So you need the operation T = T' \times (Ha)^-1 to get T.

en.wikipedia.org/wiki/Hadamard_matrix
Best,

Sebastien