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 non-linear embedding of the input signal Hilbert space into a higher dimensional Hilbert space of sesquilinear function-als so that absolute values of frame coefficients are associ-ated to relevant inner products in that space. In this space the reconstruction becomes linear and can be performed in a polynomial number of steps. 1