Recovery of K-Sparse Non-Negative Signals From K DFT Values and Their Conjugates

The goal is to reconstruct a sparse signal from some, but not all, of its Discrete Fourier Transform (DFT) values. If the signal has K non-zero and real values, a unique solution is determined by any K DFT values, their conjugates, and the DC value, if the DFT order is prime. However, no algorithm is known for this unless the K DFT values are at consecutive frequencies (a total of 2K+1 consecutive values). 1norm minimization only works if the frequencies are randomly chosen. We present a new algorithm that reconstructs a K-sparse non-negative real-valued signal from any K DFT values, their conjugates, and the DC value, provided that the DFT order is prime and less than 4K. It does not use the 1 norm or pursuit. Keywords— Sparse reconstruction Phone: 734-763-9810. Fax: 734-763-1503. Email: [email protected]. EDICS: 2-REST.