Signal synthesis from Cohen´s class of bilinear time-frequency signal representations using convex projections

The author addresses the problem of inverting a general member of the class of bilinear joint time-frequency signal representations introduced by L. Cohen (1966), i.e. obtaining the signal generating a given representation. Necessary and sufficient conditions for the exact inversion are introduced and are shown to be too restrictive to be practically useful. A constrained least-squares approach is formulated, and a solution is given by application of the method of alternating convex projections. The author also considers regularization of the method and examines some extensions of the approach