3 research outputs found
Phase Retrieval From Binary Measurements
We consider the problem of signal reconstruction from quadratic measurements
that are encoded as +1 or -1 depending on whether they exceed a predetermined
positive threshold or not. Binary measurements are fast to acquire and
inexpensive in terms of hardware. We formulate the problem of signal
reconstruction using a consistency criterion, wherein one seeks to find a
signal that is in agreement with the measurements. To enforce consistency, we
construct a convex cost using a one-sided quadratic penalty and minimize it
using an iterative accelerated projected gradient-descent (APGD) technique. The
PGD scheme reduces the cost function in each iteration, whereas incorporating
momentum into PGD, notwithstanding the lack of such a descent property,
exhibits faster convergence than PGD empirically. We refer to the resulting
algorithm as binary phase retrieval (BPR). Considering additive white noise
contamination prior to quantization, we also derive the Cramer-Rao Bound (CRB)
for the binary encoding model. Experimental results demonstrate that the BPR
algorithm yields a signal-to- reconstruction error ratio (SRER) of
approximately 25 dB in the absence of noise. In the presence of noise prior to
quantization, the SRER is within 2 to 3 dB of the CRB
Exact Phase Retrieval for a Class of 2-D Parametric Signals
We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramer-Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise