Related papers: Full Spark Frames
So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods…
Dynamic feature selection (DFS) is a machine learning framework in which features are acquired sequentially for individual samples under budget constraints. The exponential growth in the number of possible feature acquisition paths forces a…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…
We describe a flexible construction that produces triples of finitely generated, residually finite groups $M\hookrightarrow P \hookrightarrow \Gamma$, where the maps induce isomorphisms of profinite completions…
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…
Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…
We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the…
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
In near-field beam focusing for finite-sized arrays, focal shift is a non-negligible issue. The actual focal point often appears closer to the array than the predefined focal distance, significantly degrading the focusing performance of…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…