Related papers: On spurious fixed points in iterative maximum like…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

Model-based learned iterative reconstruction methods have recently been shown to outperform classical reconstruction algorithms. Applicability of these methods to large scale inverse problems is however limited by the available memory for…

In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…

The process of reconstructing quantum states from experimental measurements, accomplished through quantum state tomography (QST), plays a crucial role in verifying and benchmarking quantum devices. A key challenge of QST is to find out how…

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…

We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…

We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained…

For reconstructing large tomographic datasets fast, filtered backprojection-type or Fourier-based algorithms are still the method of choice, as they have been for decades. These robust and computationally efficient algorithms have been…

Quantum tomography approaches typically consider a set of observables which we wish to measure, design a measurement scheme which measures each of the observables and then repeats the measurements as many times as necessary. We show that…

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…

We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…

Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…