相关论文: Reconstruction of a piecewise smooth absorption co…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

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…

We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…

In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial differential equation. We show that the Bayesian formulation of…

We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…

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…

Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…

Photoacoustic tomography is a hybrid biomedical technology, which combines the advantages of acoustic and optical imaging. However, for the conventional image reconstruction method, the image quality is affected obviously by artifacts under…

This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to…

Diffuse optical breast imaging utilizes near-infrared (NIR) light propagation through tissues to assess the optical properties of tissue for the identification of abnormal tissue. This optical imaging approach is sensitive, cost-effective,…

In computed tomography, data consist of measurements of the attenuation of X-rays passing through an object. The goal is to reconstruct the linear attenuation coefficient of the object's interior. For each position of the X-ray source,…

High-precision laser interferometric instruments require optical surfaces with a close to perfect contour, as well as low scattering and absorption. Especially point absorbers are problematic because they heat up at high optical intensities…

We revisit the instability properties of the recovery of the absorption coefficient for the radiative transfer equation in the diffusive regime. To this end, we develop a rather robust framework building on [Koch-R\"uland-Salo, 2021] which…

We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT). This framework comprises of minimizing an objective…

In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…

Photo-acoustic tomography is a coupled-physics (hybrid) medical imaging modality that aims to reconstruct optical parameters in biological tissues from ultrasound measurements. As propagating light gets partially absorbed, the resulting…

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…

This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…

Reconstruction of multidimensional signals from the samples of their partial derivatives is known to be a standard problem in inverse theory. Such and similar problems routinely arise in numerous areas of applied sciences, including optical…

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…