相关论文: An Open Problem on Sparse Representations in Union…
Implicit neural representations are a promising new avenue of representing general signals by learning a continuous function that, parameterized as a neural network, maps the domain of a signal to its codomain; the mapping from spatial…
A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems. Although these systems seem superficially the same, they differ in a variety of ways; for example, how they handle a…
We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…
The hidden subgroup problem (HSP) provides a unified framework to study problems of group-theoretical nature in quantum computing such as order finding and the discrete logarithm problem. While it is known that Fourier sampling provides an…
We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is…
Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…
We establish quantitative upper and lower bounds for Schr\"odinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative version of an example, due to S.\ Boegli (Comm. Math. Phys.,…
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…
This work proposes a research problem of finding sparse solution of undetermined Linear system with some applications. Two approaches how to solve the compressive sensing problem: using l_1 approach , the l_q approach with 0 < q < 1.…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
We will give new upper bounds for the number of solutions to the inequalities of the shape $|F(x , y)| \leq h$, where $F(x , y)$ is a sparse binary form, with integer coefficients, and $h$ is a sufficiently small integer in terms of the…
Let $x\in\mathbb{C}^n$ be a spectrally sparse signal consisting of $r$ complex sinusoids with or without damping. We consider the spectral compressed sensing problem, which is about reconstructing $x$ from its partial revealed entries. By…
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key…
Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…
We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly…
In the model of randomly perturbed graphs we consider the union of a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and the binomial random graph $\mathbb{G}(n,p)$. This model was introduced by Bohman, Frieze, and…
Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then…
Sparse representation can be described in high dimensions and used in many applications, including MRI imaging and radar imaging. In some cases, methods have been proposed to solve the high-dimensional sparse representation problem, but…