I am working on a project where i am filtering the signal in time-frequency domain obtained using S-transform. I am filtering the time-frequency gray scale image, obtained using the value absolute value of the S-transform matrix. But after filtering, when I try to find the inverse S-transform, however , I have lost the imaginary component. So I am not to the correct filtered reconstructed-signal.

Reference to work done in paper :

http://www.sciencedirect.com/science/article/pii/S1959031813000936