Related papers: Proximity Operators for Phase Retrieval
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
Inverse problems consist of recovering a signal from a collection of noisy measurements. These are typically cast as optimization problems, with classic approaches using a data fidelity term and an analytic regularizer that stabilizes…
In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is…
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…
Proximal splitting-based convex optimization is a promising approach to linear inverse problems because we can use some prior knowledge of the unknown variables explicitly. An understanding of the behavior of the optimization algorithms…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…
Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
The modified Gerchberg-Saxton algorithm (MGSA) is one of the standard methods for phase retrieval. In this work we apply the MGSA in the paraxial domain. For three given physical parameters - i.e. wavelength, propagation distance and pixel…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is…
We describe the relationship between different forms of linearized expressions for the spatial distribution of intensity of X-ray projection images obtained in the Fresnel region. We prove that under the natural validity conditions some of…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
Sequential Compressive Sensing, which may be widely used in sensing devices, is a popular topic of recent research. This paper proposes an online recovery algorithm for sparse approximation of sequential compressive sensing. Several…
We consider the problem of estimating the sparse time-varying parameter vectors of a point process model in an online fashion, where the observations and inputs respectively consist of binary and continuous time series. We construct a novel…
Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…
In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear…
Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different…
We present in this work alternative analytic formulations for the fan-beam tomographic backprojection operation and its associated adjoint transform in standard (equiangular) and linear (equidistant) detector geometries. The proposed…