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Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
Le Cam's method (or the two-point method) is a commonly used tool for obtaining statistical lower bound and especially popular for functional estimation problems. This work aims to explain and give conditions for the tightness of Le Cam's…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
A message composed of packets is transmitted using erasure and channel coding over a fading channel with no feedback. For this scenario, the paper explores the trade-off between the redundancies allocated to the packet-level erasure code…
Recently, the benefit of heavily overparameterized models has been observed in machine learning tasks: models with enough capacity to easily cross the \emph{interpolation threshold} improve in generalization error compared to the classical…
This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in…
This manuscript focuses on the construction of compactly supported dual Gabor frames in $L^2(\mathbb{R})$. The performance of the constructed dual frames is analysed for Gabor systems generated by B-splines and exponential B-splines of…
Finding the optimal size of deep learning models is very actual and of broad impact, especially in energy-saving schemes. Very recently, an unexpected phenomenon, the ``double descent'', has caught the attention of the deep learning…
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…
Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by…
Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…
Correcting the optical aberrations and the manufacturing deviations of cameras is a challenging task. Due to the limitation on volume and the demand for mass production, existing mobile terminals cannot rectify optical degradation. In this…
The advancement of new digital image sensors has enabled the design of exposure multiplexing schemes where a single image capture can have multiple exposures and conversion gains in an interlaced format, similar to that of a Bayer color…
The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Coherent imaging systems, such as medical ultrasound and synthetic aperture radar (SAR), are subject to corruption from speckle due to sub-resolution scatterers. Since speckle is multiplicative in nature, the constituent image regions…
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…
The joint design of the optical system and the downstream algorithm is a challenging and promising task. Due to the demand for balancing the global optimal of imaging systems and the computational cost of physical simulation, existing…
We link optimal filtering for hidden Markov models to the notion of duality for Markov processes. We show that when the signal is dual to a process that has two components, one deterministic and one a pure death process, and with respect to…