相关论文: Reconstruction algorithms for source term recovery…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…
Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…
The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore,…
In groundwater contaminant remediation and risk assessment, it is important to identify parameters of the contaminant source and hydraulic conductivity field by solving an inverse problem. However, if the dimensionality of the inverse…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…
Phase retrieval aims to recover a signal from intensity-only measurements, a fundamental problem in many fields such as imaging, holography, optical computing, crystallography, and microscopy. Although there are several well-known phase…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
End-to-end generative methods are considered a more promising solution for image restoration in physics-based vision compared with the traditional deconstructive methods based on handcrafted composition models. However, existing generative…
In many applications, a signal is deformed by well-understood dynamics before it can be measured. For example, when a pollutant enters a river, it immediately begins dispersing, flowing, settling, and reacting. If the pollutant enters at a…
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…