Related papers: Recovery from Power Sums
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
The paper investigates recoverability of sequences from their periodic subsequences and offers some modification of the approach suggested in papers arXiv:1605.00414 and arXiv:1803.02233. It is shown that there exists a class of sequences…
Recently, there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. Mostly, it has been done by proving new and sometimes optimal upper bounds for both linear sampling recovery and for…
We investigate the problem of recovering jointly $r$-rank and $s$-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that $m \asymp r s…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
We study a combinatorial notion where given a set of lattice points one takes the set of all sums of subsets of a fixed size, and we ask if the given set comes from a convex lattice polytope whether the resulting set also comes from a…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real or complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
We study the quantitative relationship between the cones of nonnegative polynomials, cones of sums of squares and cones of sums of powers of linear forms. We derive bounds on the volumes (raised to the power reciprocal to the ambient…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations. However, it is a significant challenge for the system with long-range interactions. We employ symbolic regression to regress…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
We present two new methods for multivariate exponential analysis. In [7], we developed a new algorithm for reconstruction of univariate exponential sums by exploiting the rational structure of their Fourier coefficients and reconstructing…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely…