Quantization-Aware Phase Retrieval

by   Subhadip Mukherjee, et al.
indian institute of science

We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in many practical applications. We develop a rank-1 projection algorithm that recovers the signal subject to ensuring consistency with the measurement, that is, the recovered signal when encoded must yield the same set of measurements that one started with. The rank-1 projection stems from the idea of lifting, originally proposed in the context of PhaseLift. The consistency criterion is enforced using a one-sided quadratic cost. We also determine the probability with which different vectors lead to the same set of quantized measurements, which makes it impossible to resolve them. Naturally, this probability depends on how correlated such vectors are, and how coarsely/finely the measurements get quantized. The proposed algorithm is also capable of incorporating a sparsity constraint on the signal. An analysis of the cost function reveals that it is bounded, both above and below, by functions that are dependent on how well correlated the estimate is with the ground truth. We also derive the Cramér-Rao lower bound (CRB) on the achievable reconstruction accuracy. A comparison with the state-of-the- art algorithms shows that the proposed algorithm has a higher reconstruction accuracy and is about 2 to 3 dB away from the CRB. The edge, in terms of the reconstruction signal-to-noise ratio, over the competing algorithms is higher (about 5 to 6 dB) when the quantization is coarse.


page 10

page 13


Taking the edge off quantization: projected back projection in dithered compressive sensing

Quantized compressive sensing (QCS) deals with the problem of representi...

A Fast and Provable Algorithm for Sparse Phase Retrieval

We study the sparse phase retrieval problem, which aims to recover a spa...

Injectivity of Multi-window Gabor Phase Retrieval

In many signal processing problems arising in practical applications, we...

Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering

In Compressive Sensing theory and its applications, quantization of sign...

DeepFPC: Deep Unfolding of a Fixed-Point Continuation Algorithm for Sparse Signal Recovery from Quantized Measurements

We present DeepFPC, a novel deep neural network designed by unfolding th...

The Generalized Lasso for Sub-gaussian Measurements with Dithered Quantization

In the problem of structured signal recovery from high-dimensional linea...

Please sign up or login with your details

Forgot password? Click here to reset