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Digital twins are fundamental to the development of autonomous driving and embodied artificial intelligence. However, achieving high-granularity surface reconstruction and high-fidelity rendering remains a challenge. Gaussian splatting…
In this work we investigate numerically the reconstruction approach proposed in Goncharov, Novikov, 2016, for weighted ray transforms (weighted Radon transforms along oriented straight lines) in 3D. In particular, the approach is based on a…
Recent advancements in 3D robotic manipulation have improved grasping of everyday objects, but transparent and specular materials remain challenging due to depth sensing limitations. While several 3D reconstruction and depth completion…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
Let $X$ and $Y$ be Hilbert spaces, and $\mathbf{K}: \text{dom} \mathbf{K} \subset X \to Y$ a bounded linear operator. This paper addresses the inverse problem $\mathbf{K}x = y$, where exact data $y$ is replaced by noisy data $y^\delta$…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
In an earlier paper, we studied solutions g to convolution equations of the form a_d*g^{*d}+a_{d-1}*g^{*(d-1)}+...+a_1*g+a_0=0, where a_0, ..., a_d are given arithmetic functions associated with Dirichlet series which converge on some right…
Neural Radiance Fields (NeRFs) have emerged as a powerful paradigm for multi-view reconstruction, complementing classical photogrammetric pipelines based on Structure-from-Motion (SfM) and Multi-View Stereo (MVS). However, their reliability…
In this paper we simplify and otherwise improve the local resolution of singularities algorithm of [G1]-[G3], providing a local resolution of singularities method that works for functions with convergent power series over an arbitrary local…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to…
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
This paper uses reconstruction algebras to construct simultaneous resolution of determinantal surfaces. The main new difference to the classical case is that, in addition to the quiver of the reconstruction algebra, certain noncommutative…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
Data acquisition in array signal processing (ASP) is costly because achieving high angular and range resolutions necessitates large antenna apertures and wide frequency bandwidths, respectively. The data requirements for ASP problems grow…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…