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We demonstrate a different scheme to perform optical sectioning of a sample based on the concept of induced coherence [Zou et al., Phys. Rev. Lett. 67, 318 (1991)]. This can be viewed as a different type of optical coherence tomography…

We develop and implement a compressive reconstruction method for tomographic recovery of refractive index distribution for weakly attenuating objects in a microfocus X-ray system. This is achieved through the development of a discretized…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…

We propose a method to reduce non-uniform sample variance to a predetermined target level. The proposed space-variant filter can equalize variance of the non-stationary signal, or vary filtering strength based on image features, such as…

Non-line-of-sight imaging has attracted more attentions for its wide applications.Even though ultrasensitive cameras or detectors with high time-resolution are available, current back-projection methods are still powerless to acquire a…

We adapt the rectangular splitting technique of Paterson and Stockmeyer to the problem of evaluating terms in holonomic sequences that depend on a parameter. This approach allows computing the $n$-th term in a recurrent sequence of suitable…

Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…

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…

A novel partial order is defined on the space of digraphs or hypergraphs, based on assessing the cost of producing a graph via a sequence of elementary transformations. Leveraging work by Knuth and Skilling on the foundations of inference,…

Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. In this paper we address the application of CS to the scenario of progressive acquisition of 2D visual…

This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or…

We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in…

In NMR spectroscopy, undersampling in the indirect dimensions causes reconstruction artifacts whose size can be bounded using the so-called {\it coherence}. In experiments with multiple indirect dimensions, new undersampling approaches were…

A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…

We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms. Our approach not only allows for the anti-aliasing of the images but also…

This paper investigates signal prediction through the perfect reconstruction of signals from shift-invariant spaces using nonuniform samples of both the signal and its derivatives. The key advantage of derivative sampling is its ability to…

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…