Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork
76
0
0.0
(
0
)
Added by
Chang-Jen Wang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half century. Recent advances in deep learning have opened up a new possibility for robust and fast PR. An emerging technique, called deep unfolding, provides a systematic connection between conventional model-based iterative algorithms and modern data-based deep learning. Unfolded algorithms, powered by data learning, have shown remarkable performance and convergence speed improvement over the original algorithms. Despite their potential, most existing unfolded algorithms are strictly confined to a fixed number of iterations when employing layer-dependent parameters. In this study, we develop a novel framework for deep unfolding to overcome the existing limitations. Even if our framework can be widely applied to general inverse problems, we take PR as an example in the paper. Our development is based on an unfolded generalized expectation consistent signal recovery (GEC-SR) algorithm, wherein damping factors are left for data-driven learning. In particular, we introduce a hypernetwork to generate the damping factors for GEC-SR. Instead of directly learning a set of optimal damping factors, the hypernetwork learns how to generate the optimal damping factors according to the clinical settings, thus ensuring its adaptivity to different scenarios. To make the hypernetwork work adapt to varying layer numbers, we use a recurrent architecture to develop a dynamic hypernetwork, which generates a damping factor that can vary online across layers. We also exploit a self-attention mechanism to enhance the robustness of the hypernetwork. Extensive experiments show that the proposed algorithm outperforms existing ones in convergence speed and accuracy, and still works well under very harsh settings, that many classical PR algorithms unstable or even fail.
rate research
Read More
In this paper, we propose a generalized expectation consistent signal recovery algorithm to estimate the signal $mathbf{x}$ from the nonlinear measurements of a linear transform output $mathbf{z}=mathbf{A}mathbf{x}$. This estimation problem has been encountered in many applications, such as communications with front-end impairments, compressed sensing, and phase retrieval. The proposed algorithm extends the prior art called generalized turbo signal recovery from a partial discrete Fourier transform matrix $mathbf{A}$ to a class of general matrices. Numerical results show the excellent agreement of the proposed algorithm with the theoretical Bayesian-optimal estimator derived using the replica method.
In phase retrieval we want to recover an unknown signal $boldsymbol xinmathbb C^d$ from $n$ quadratic measurements of the form $y_i = |langle{boldsymbol a}_i,{boldsymbol x}rangle|^2+w_i$ where $boldsymbol a_iin mathbb C^d$ are known sensing vectors and $w_i$ is measurement noise. We ask the following weak recovery question: what is the minimum number of measurements $n$ needed to produce an estimator $hat{boldsymbol x}(boldsymbol y)$ that is positively correlated with the signal $boldsymbol x$? We consider the case of Gaussian vectors $boldsymbol a_i$. We prove that - in the high-dimensional limit - a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For $nle d-o(d)$ no estimator can do significantly better than random and achieve a strictly positive correlation. For $nge d+o(d)$ a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theory arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper and lower bound generalize beyond phase retrieval to measurements $y_i$ produced according to a generalized linear model. As a byproduct of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm.
The reconstruction of sparse signal is an active area of research. Different from a typical i.i.d. assumption, this paper considers a non-independent prior of group structure. For this more practical setup, we propose EM-aided HyGEC, a new algorithm to address the stability issue and the hyper-parameter issue facing the other algorithms. The instability problem results from the ill condition of the transform matrix, while the unavailability of the hyper-parameters is a ground truth that their values are not known beforehand. The proposed algorithm is built on the paradigm of HyGAMP (proposed by Rangan et al.) but we replace its inner engine, the GAMP, by a matrix-insensitive alternative, the GEC, so that the first issue is solved. For the second issue, we take expectation-maximization as an outer loop, and together with the inner engine HyGEC, we learn the value of the hyper-parameters. Effectiveness of the proposed algorithm is also verified by means of numerical simulations.
We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation. We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design measurements, we show that PhaseLift can reconstruct all unitary matrices, using a near-optimal number of measurements. This extends previous work on PhaseLift using spherical 4-designs. In the case of unitary 2-design measurements, we show that PhaseLift still works pretty well on average: it recovers almost all signals, up to a constant additive error, using a near-optimal number of measurements. These 2-design measurements are convenient for quantum process tomography, as they can be implemented via randomized benchmarking techniques. This is the first positive result on PhaseLift using 2-designs.
We study the problem of indoor localization using commodity WiFi channel state information (CSI) measurements. The accuracy of methods developed to address this problem is limited by the overall bandwidth used by the WiFi device as well as various types of signal distortions imposed by the underlying hardware. In this paper, we propose a localization method that performs channel impulse response (CIR) estimation by splicing measured CSI over multiple WiFi bands. In order to overcome hardware-induced phase distortions, we propose a phase retrieval (PR) scheme that only uses CSI magnitude values to estimate the CIR. To achieve high localization accuracy, the PR scheme involves a sparse recovery step, which exploits the fact that the CIR is sparse over the delay domain, due to the small number of contributing signal paths in an indoor environment. Simulation results indicate that our approach outperforms the state of the art by an order of magnitude (cm-level localization accuracy) for more than 90% of the trials and for various SNR regimes.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
