A Nonlinear Reconstruction Algorithm from Absolute Value of Frame Coefficients for Low Redundancy Frames

In this paper we present a signal reconstruction algorithm from absolute value of frame coefficients that requires a relatively low redundancy. The basic idea is to use a nonlinear embedding of the input signal Hilbert space into a higher dimensional Hilbert space of sesquilinear functionals so that absolute values of frame coefficients are associated to relevant inner products in that space. In this space the reconstructionbecomes linear and can be performedin a polynomial number of steps.