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In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…
Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for…
Assuming linearity of the perturbations at the time of decoupling, we reconstruct the primordial scalar potential from the temperature and polarization anisotropies in the cosmic microwave background radiation. In doing so we derive an…
Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition…
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
We present a novel approach for reconstructing the projected mass distribution of clusters of galaxies from sparse and noisy weak gravitational lensing shear data. The reconstructions are regularised using knowledge gained from numerical…
We extend to large scales a method proposed in previous work that reconstructs non-parametrically the primordial power spectrum from cosmic microwave background data at high resolution. The improvement is necessary to account for the…
Phase retrieval in inline holography is a fundamental yet ill-posed inverse problem due to the nonlinear coupling between amplitude and phase in coherent imaging. We present a novel off-the-shelf solution that leverages a diffusion model…
We present a general framework for reconstructing effective Hamiltonians from known gravitational energy density profiles in curved spacetime. Starting from local thermal equilibrium and Liouville dynamics, we establish an inverse procedure…
With the recently published Cosmic Microwave Background data from Planck we address the optimized binning of the primordial power spectrum. As an important modification to the usual binning of the primordial spectrum, along with the…
In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can…
We investigate the problem of reconstructing signals from a subsampled convolution of their modulated versions and a known filter. The problem is studied as applies to specific imaging systems relying on spatial phase modulation by randomly…
We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling…
In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take…
We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running…