Related papers: Resolution and Robustness Bounds for Reconstructiv…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
Light spectra are a very important source of information for diverse classification problems, e.g., for discrimination of materials. To lower the cost for acquiring this information, multispectral cameras are used. Several techniques exist…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability…
In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
Laser speckle, the granular intensity pattern arising from random optical interference, provides a high-dimensional encoding of spectral information that can be exploited for precision metrology. Speckle-based spectrometers have advanced…
Nuclear Magnetic Resonance (NMR) spectroscopy is a crucial analytical technique used for molecular structure elucidation, with applications spanning chemistry, biology, materials science, and medicine. However, the frequency resolution of…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate…
In deep tissue photoacoustic imaging the spatial resolution is inherently limited by the acoustic wavelength. Recently, it was demonstrated that it is possible to surpass the acoustic diffraction limit by analyzing fluctuations in a set of…
This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Optical spectrometers have propelled scientific and technological advancements in a wide range of fields. While sophisticated systems with excellent performance metrics are serving well in controlled laboratory environments, many…
Consistent reconstruction is a method for producing an estimate $\widetilde{x} \in \mathbb{R}^d$ of a signal $x\in \mathbb{R}^d$ if one is given a collection of $N$ noisy linear measurements $q_n = \langle x, \varphi_n \rangle +…
Modern deep learning reconstruction algorithms generate impressively realistic scans from sparse inputs, but can often produce significant inaccuracies. This makes it difficult to provide statistically guaranteed claims about the true state…
Speckle based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown,…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…