Phase Retrieval by Alternating Minimization With Random Initialization
نویسندگان
چکیده
منابع مشابه
Alternating minimization for dictionary learning with random initialization
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples y, y, . . . , y into an appropriate basis (dictionary) A∗ and sparse vectors x1∗, . . . , xn∗. Our algorithm is a simple alternating minimization procedure that switches between l1 minimization and gradient ...
متن کاملGradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest x ∈ R from m quadratic equations / samples yi = (ai x), 1 ≤ i ≤ m. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficiency of gradient descent (or Wirtinger flow) designed for the nonconv...
متن کاملPhase retrieval with random phase illumination.
This paper presents a detailed numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio σ=4 determines a unique phasing solution up to a global phase factor. Under this condition, the standard phasing algorithms converge rapidly to the true solution without stagnation. Excellent approx...
متن کاملAn alternating optimization approach for phase retrieval
In this paper, we address the problem of phase retrieval to recover a signal from the magnitude of its Fourier transform. In many applications of phase retrieval, the signals encountered are naturally sparse. In this work, we consider the case where the signal is sparse under the assumption that few components are nonzero. We exploit further the sparse nature of the signals and propose a two st...
متن کاملUndersampled Phase Retrieval via Majorization-Minimization
In the undersampled phase retrieval problem, the goal is to recover an N -dimensional complex signal x from only M < N noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce the number of required measurements since a recent theory established that M ≈ 4N intensity measurements are necessary and sufficient to recover a generic signal x. In th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2020
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2020.2971211