Related papers: Numerically erasure-robust frames
Data erasure can often occur in communication. Guarding against erasures involves redundancy in data representation. Mathematically this may be achieved by redundancy through the use of frames. One way to measure the robustness of a frame…
In this paper, we investigate the robustness of structured frames to measurement noise and erasures, with the focus on Gabor frames $(g, \Lambda)$ with arbitrary sets of time-frequency shifts $\Lambda$. This property of frames is important…
We propose a new approach to the problem of recovering signal from frame coefficients with erasures. Such problems arise naturally from applications where some of the coefficients could be corrupted or erased during the data transmission.…
We consider finite frames with high redundancy so that if half the terms transmitted from the sender are randomly deleted during transmission, then on average, the receiver can still recover the signal to within a high level of accuracy.…
In this paper we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased coefficients are indexed by a finite set $E$. Starting from a frame $(x_n)_{n=1}^\infty$ and its arbitrary dual frame, we…
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…
In ground based infrared imaging a well-known technique to reduce the influence of thermal and background noise is chopping and nodding, where four different signals of the same object are recorded from which the object is reconstructed…
Accurate 3D reconstruction from multi-view images is essential for downstream robotic tasks such as navigation, manipulation, and environment understanding. However, obtaining precise camera poses in real-world settings remains challenging,…
Event cameras offer many advantages over standard cameras due to their distinctive principle of operation: low power, low latency, high temporal resolution and high dynamic range. Nonetheless, the success of many downstream visual…
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and erasures, and as such, have great potential…
We give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate…
Burst super-resolution (BurstSR) aims at reconstructing a high-resolution (HR) image from a sequence of low-resolution (LR) and noisy images, which is conducive to enhancing the imaging effects of smartphones with limited sensors. The main…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
In this paper we introduce a new probabilistic model for optimizing erasures occurring in data transmission using Parseval frames and a sequence of Bernoulli random variables associated to the channels of the transmission. We establish…
In recent years, video analysis tools for automatically extracting meaningful information from videos are widely studied and deployed. Because most of them use deep neural networks which are computationally expensive, feeding only a subset…
Implicit Neural Representations (INRs) encode discrete signals in a continuous manner using neural networks, demonstrating significant value across various multimedia applications. However, the vulnerability of INRs presents a critical…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
In the field of compressed sensing, a key problem remains open: to explicitly construct matrices with the restricted isometry property (RIP) whose performance rivals those generated using random matrix theory. In short, RIP involves…