DOLPHIn - Dictionary Learning for Phase Retrieval

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method

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

Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning

Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the measured signal admits a sparse representation over an unknown dictionary. The task is to jointly estimate the dictionary and the sparse representation from magnitude-only measurements. To this end, we study two complementary formulations and develop efficient parallel algorithms by extending the successive convex approximation framework using a smooth majorization. The first algorithm is termed compact-SCAphase and is preferable in the case of less diverse mixture models. It employs a compact formulation that avoids the use of auxiliary variables. The proposed algorithm is highly scalable and has reduced parameter tuning cost. The second algorithm, referred to as SCAphase, uses auxiliary variables and is favorable in the case of highly diverse mixture models. It also renders simple incorporation of additional side constraints. The performance of both methods is evaluated when applied to blind sparse channel estimation from subband magnitude measurements in a multi-antenna random access network. Simulation results demonstrate the efficiency of the proposed techniques compared to state-of-the-art methods.Comment: This work has been submitted to the IEEE Transactions on Signal Processing for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Automated photo-identification of cetaceans : An integrated software solution

This study investigates current techniques used for automated photo-identification of cetaceans (i.e. dolphins and whales). The primary focus constitutes various techniques that can be applied to identify and extract dorsal fins from digital photographs. A comprehensive analysis of these techniques demonstrates the most effective software solution. To further support this analysis, four prototypes are developed to demonstrate the effectiveness of each technique in a practical environment. The analysis bases its final conclusions on test results generated from these prototype software examples. Final conclusions provide recommendations for an effective, accurate, and practical software solution. This software solution allows dorsal fins to be easily extracted from digital photographs and identified through the use of computer automated methods