arXiv subjects

Grigory Solomatov

Publications and source records attributed to Grigory Solomatov.

8 recordsLinked to original sources

arXiv2026

Underwater Color Restoration with Vanishing Uncertainty

Underwater color restoration promises to unlock color as a reliable signal for aquatic sciences, but achieving this with scientific confidence remains out of reach. Current methods are validated almost exclusively on an empirical basis, which provides confidence only to the extent that the vast diversity of possible visibility conditions is covered with end-to-end testing using a known ground truth. This is exacerbated by color restoration being a fatally ill-posed problem when considered in full mathematical generality, requiring additional constraints to narrow the solution to a finite uncertainty interval. The gap between which constraints suffice in theory and which constraints are satisfied by real-world data is poorly understood, making it unclear whether existing methods are solving a problem that is actually solvable. In this article, we investigate the theoretical side of this gap, identifying idealized conditions which guarantee bounded uncertainty that converges to zero as the spatial resolution of the camera increases.

eess.IV↗

arXiv2026

Conditions for well-posed color recovery in scattering media

Recovering scene color from images captured in scattering media is a fundamental inverse problem in optical imaging. Yet the problem is intrinsically ill-posed as multiple solutions can explain the same observation, and prediction error cannot be controlled without understanding the space of candidate solutions. Here, we present sufficient conditions under which color recovery in a scattering medium becomes well-posed. Observing that ill-posedness stems from (i) projection of spectral signals onto pixel intensities, and (ii) unknown medium parameters, we demonstrate that sensor improvements alone cannot resolve medium-induced distortions without additional constraints. We identify recovery patterns, cross-pixel relationships that naturally occur in images, and prove, for an ideal hyperspectral camera, that they restrict the solution to a unique candidate. This opens the door to a new class of vision algorithms grounded in first principles, enabling quantitative analysis of images in scattering environments.

cs.CV↗

arXiv2023

Spectral Sensitivity Estimation Without a Camera

A number of problems in computer vision and related fields would be mitigated if camera spectral sensitivities were known. As consumer cameras are not designed for high-precision visual tasks, manufacturers do not disclose spectral sensitivities. Their estimation requires a costly optical setup, which triggered researchers to come up with numerous indirect methods that aim to lower cost and complexity by using color targets. However, the use of color targets gives rise to new complications that make the estimation more difficult, and consequently, there currently exists no simple, low-cost, robust go-to method for spectral sensitivity estimation. Furthermore, even if not limited by hardware or cost, researchers frequently work with imagery from multiple cameras that they do not have in their possession. To provide a practical solution to this problem, we propose a framework for spectral sensitivity estimation that not only does not require any hardware, but also does not require physical access to the camera itself. Similar to other work, we formulate an optimization problem that minimizes a two-term objective function: a camera-specific term from a system of equations, and a universal term that bounds the solution space. Different than other work, we use publicly available high-quality calibration data to construct both terms. We use the colorimetric mapping matrices provided by the Adobe DNG Converter to formulate the camera-specific system of equations, and constrain the solutions using an autoencoder trained on a database of ground-truth curves. On average, we achieve reconstruction errors as low as those that can arise due to manufacturing imperfections between two copies of the same camera. We provide our code and predicted sensitivities for 1,000+ cameras, and discuss which tasks can become trivial when camera responses are available.

eess.IV↗

arXiv2022

Fast Decoding of AG Codes

We present an efficient list decoding algorithm in the style of Guruswami-Sudan for algebraic geometry codes. Our decoder can decode any such code using $\tilde{\mathcal O}(s\ell^ωμ^{ω-1}(n+g))$ operations in the underlying finite field, where $n$ is the code length, $g$ is the genus of the function field used to construct the code, $s$ is the multiplicity parameter, $\ell$ is the designed list size and $μ$ is the smallest positive element in the Weierstrass semigroup at some chosen place; the "soft-O" notation $\tilde{\mathcal O}(\cdot)$ is similar to the "big-O" notation ${\mathcal O}(\cdot)$, but ignores logarithmic factors. For the interpolation step, which constitutes the computational bottleneck of our approach, we use known algorithms for univariate polynomial matrices, while the root-finding step is solved using existing algorithms for root-finding over univariate power series.

cs.IT↗

arXiv2021

Improved Power Decoding of Algebraic Geometry Codes

Power decoding is a partial decoding paradigm for arbitrary algebraic geometry codes for decoding beyond half the minimum distance, which usually returns the unique closest codeword, but in rare cases fails to return anything. The original version decodes roughly up to the Sudan radius, while an improved version decodes up to the Johnson radius, but has so far been described only for Reed--Solomon and one-point Hermitian codes. In this paper we show how the improved version can be applied to any algebraic geometry code.

math.AG↗

arXiv2020

Fast Encoding of AG Codes over $C_{ab}$ Curves

We investigate algorithms for encoding of one-point algebraic geometry (AG) codes over certain plane curves called $C_{ab}$ curves, as well as algorithms for inverting the encoding map, which we call "unencoding". Some $C_{ab}$ curves have many points or are even maximal, e.g. the Hermitian curve. Our encoding resp. unencoding algorithms have complexity $\tilde{O}(n^{3/2})$ resp. $\tilde{O}(qn)$ for AG codes over any $C_{ab}$ curve satisfying very mild assumptions, where $n$ is the code length and $q$ the base field size, and $\tilde{O}$ ignores constants and logarithmic factors in the estimate. For codes over curves whose evaluation points lie on a grid-like structure, notably the Hermitian curve and norm-trace curves, we show that our algorithms have quasi-linear time complexity $\tilde{O}(n)$ for both operations. For infinite families of curves whose number of points is a constant factor away from the Hasse--Weil bound, our encoding algorithm has complexity $\tilde{O}(n^{5/4})$ while unencoding has $\tilde{O}(n^{3/2})$.

math.AG↗

arXiv2020

Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation

Suppose $\mathbb{K}$ is a large enough field and $\mathcal{P} \subset \mathbb{K}^2$ is a fixed, generic set of points which is available for precomputation. We introduce a technique called \emph{reshaping} which allows us to design quasi-linear algorithms for both: computing the evaluations of an input polynomial $f \in \mathbb{K}[x,y]$ at all points of $\mathcal{P}$; and computing an interpolant $f \in \mathbb{K}[x,y]$ which takes prescribed values on $\mathcal{P}$ and satisfies an input $y$-degree bound. Our genericity assumption is explicit and we prove that it holds for most point sets over a large enough field. If $\mathcal{P}$ violates the assumption, our algorithms still work and the performance degrades smoothly according to a distance from being generic. To show that the reshaping technique may have an impact on other related problems, we apply it to modular composition: suppose generic polynomials $M \in \mathbb{K}[x]$ and $A \in \mathbb{K}[x]$ are available for precomputation, then given an input $f \in \mathbb{K}[x,y]$ we show how to compute $f(x, A(x)) \operatorname{rem} M(x)$ in quasi-linear time.

cs.SC↗

arXiv2018

Computing Popov and Hermite forms of rectangular polynomial matrices

We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are known. Here, we present deterministic, fast algorithms for rectangular input matrices. The obtained cost bound for the Popov form matches the previous best known randomized algorithm, while the cost bound for the Hermite form improves on the previous best known ones by a factor which is at least the largest dimension of the input matrix.

cs.SC↗