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Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored…
Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…
Neural compression methods are gaining popularity due to their superior rate-distortion performance over traditional methods, even at extremely low bitrates below 0.1 bpp. As deep learning architectures, these models are prone to bias…
Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging…
Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are…
Optical phase-modulated fringe-patterns are usually digitized with XxY pixels and 8 bits/pixel (or higher) gray-levels. The digitized 8 bits/pixel are raw-data bits, not Shannon information bits. Here we show that noisy fringe-patterns…
Removal or cancellation of noise has wide-spread applications for imaging and acoustics. In every-day-life applications, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however,…
This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory…
A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable multipartite…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…
Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper we show that a wiser method of duplication entails…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
Consider a lossy compression system with $\ell$ distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under…
Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more time efficient and are thus widely used in large scale storage…