Related papers: Sampling and Reconstruction in Different Subspaces…
Increasing spatial image resolution is an often required, yet challenging task in image acquisition. Recently, it has been shown that it is possible to obtain a high resolution image by covering a low resolution sensor with a non-regular…
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ allows for a linear and stable reconstruction of any vector $x\in H$ from the linear measurements $(\langle x,x_j\rangle)_{j\in J}$. However, there are many situations where some information…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
A central challenge in data visualization is to understand which data samples are required to generate an image of a data set in which the relevant information is encoded. In this work, we make a first step towards answering the question of…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
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…
A method of modelling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The…
Reconstructing a 3D shape based on a single sketch image is challenging due to the large domain gap between a sparse, irregular sketch and a regular, dense 3D shape. Existing works try to employ the global feature extracted from sketch to…
We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the…
The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation…
Compression is an important task for many practical applications of light fields. Although previous work has proposed numerous methods for efficient light field compression, the effect of view selection on this task is not well exploited.…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
In this paper we broadly consider techniques which utilize projections on rays for data collection, with particular emphasis on optical techniques. We formulate a variety of imaging techniques as either special cases or extensions of…