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We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Ptychography has become prominent at synchrotron facilities worldwide for characterizing biological and material specimens' topological structures and properties at the nanometer or atomic scale, due to its lens - less, highly quantitative…
Ptychography is an attractive advance of coherent diffraction imaging (CDI), which can provide high lateral resolution and wide field of view. The theoretical resolution of ptychography is dose-limited, therefore making ptychography…
3D reconstruction of medical images is a key technology in medical image analysis and clinical diagnosis, providing structural visualization support for disease assessment and surgical planning. Traditional methods are computationally…
Ptychography is a popular technique to achieve diffraction limited resolution images of a two or three dimensional sample using high frame rate detectors. We introduce a relaxation of common projection algorithms to account for…
In this paper, we introduce a method to build an adapted mesh representation of a 3D object for X-Ray tomography reconstruction. Using this representation, we provide means to reduce the computational cost of reconstruction by way of…
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…
Microscopic fringe projection profilometry is a powerful 3D measurement technique with a theoretical measurement accuracy better than one micron provided that the measured targets can be imaged with good fringe visibility. However,…
Recently, efforts have been made to improve ptychography phase retrieval algorithms so that they are more robust against noise. Often the algorithm is adapted by changing the cost functional that needs to be minimized. In particular, it has…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
The MARS scanner is designed for the x-ray spectroscopic study of samples with the aid of computer tomography methods. Computer tomography allows the reconstruction of slices of an investigated sample using a set of shadow projections…
In this paper we introduce a method for resolving multi-parameter likelihoods by fixing all parameter values, but two. Evaluation of those two variables is followed by iteratively cycling through each of the parameters in turn until…
We present \code{phaser}, an open-source Python package that provides a unified interface to both conventional and gradient descent-based ptychographic algorithms. Features such as mixed-state probe, probe position correction, and…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
In this paper, we propose a computational framework for 3D volume reconstruction from 2D histological slices using registration algorithms in feature space. To improve the quality of reconstructed 3D volume, first, intensity variations in…
In Single Photon Emission Computed Tomography (SPECT), 3D images usually reconstructed by performing a set of bidimensional (2D) analytical or iterative reconstructions can also be reconstructed using an iterative reconstruction algorithm…
3D Lidar imaging can be a challenging modality when using multiple wavelengths, or when imaging in high noise environments (e.g., imaging through obscurants). This paper presents a hierarchical Bayesian algorithm for the robust…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
MRI is an indispensable clinical tool, offering a rich variety of tissue contrasts to support broad diagnostic and research applications. Clinical exams routinely acquire multiple structural sequences that provide complementary information…
The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, information from previous longitudinal scans of the same…