Related papers: Spectral Sparsification by Deterministic Discrepan…
Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the…
Rain streaks manifest as directional and frequency-concentrated structures that overlap across multiple scales, making single-image rain removal particularly challenging. While diffusion-based restoration models provide a powerful framework…
Differential optical absorption spectroscopy (DOAS) is a powerful tool for detecting and quantifying trace gases in atmospheric chemistry \cite{Platt_Stutz08}. DOAS spectra consist of a linear combination of complex multi-peak multi-scale…
We introduce dissipative spectroscopy as a framework for extracting spectral information from quantum systems via controlled dissipation. By establishing a general dissipative response theory applicable to both Markovian and non-Markovian…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
We address the subset selection problem for matrices, where the goal is to select a subset of $k$ columns from a "short-and-fat" matrix $X \in \mathbb{R}^{m \times n}$, such that the pseudoinverse of the sampled submatrix has as small…
I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE…
We refine the cycle-walk (Fourier) template of Gnacik and the author to quantify when a~$\delta$-Sule\u{\i}manova spectrum $(1,\lambda_2,\dots,\lambda_n)$ (with $\lambda_j\le 0$) is realised by a symmetric doubly stochastic matrix. For the…
As a new generation of large-sky spectroscopic surveys comes online, the enormous data volume poses unprecedented challenges in classifying spectra. Modern unsupervised techniques have the power to group spectra based on their dominant…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to…
Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…
The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the…
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for…
Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…
We develop a linear algebraic framework for the shape-from-shading problem, because tensors arise when scalar (e.g. image) and vector (e.g. surface normal) fields are differentiated multiple times. Using this framework, we first investigate…
The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…
A recent palette sparsification theorem of Assadi, Chen, and Khanna [SODA'19] states that in every $n$-vertex graph $G$ with maximum degree $\Delta$, sampling $O(\log{n})$ colors per each vertex independently from $\Delta+1$ colors almost…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
Spectral unmixing (SU) expresses the mixed pixels existed in hyperspectral images as the product of endmember and abundance, which has been widely used in hyperspectral imagery analysis. However, the influence of light, acquisition…