Related papers: Statistical Noise Analysis in SENSE Parallel MRI
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise.…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…
Non-Gaussian impulsive noise (IN) with memory exists in many practical applications. When it is mixed with white Gaussian noise (WGN), the resultant mixed noise will be bursty. The performance of communication systems will degrade…
Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…
Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time-conditioning mechanisms,…
We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking…
Noisy supervision refers to supervising image restoration learning with noisy targets. It can alleviate the data collection burden and enhance the practical applicability of deep learning techniques. However, existing methods suffer from…
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…
We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…
Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture…
Deep learning (DL) has shown promise for faster, high quality accelerated MRI reconstruction. However, supervised DL methods depend on extensive amounts of fully-sampled (labeled) data and are sensitive to out-of-distribution (OOD) shifts,…
In x-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is…
Recent diffusion models have achieved promising performances in audio-denoising tasks. The unique property of the reverse process could recover clean signals. However, the distribution of real-world noises does not comply with a single…