Related papers: Blind Deconvolution via Maximum Kurtosis Adaptive …
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
Blind deconvolution over graphs involves using (observed) output graph signals to obtain both the inputs (sources) as well as the filter that drives (models) the graph diffusion process. This is an ill-posed problem that requires additional…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
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…
We consider the problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach.…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
This paper investigates system identification problems with Gaussian inputs and quantized observations under fixed thresholds. By reinterpreting the nonlinear effects induced by quantization as the product of the unknown parameter and an…
The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…
This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging,…
This paper considers the blind deconvolution of multiple modulated signals, and an arbitrary filter. Multiple inputs $\boldsymbol{s}_1, \boldsymbol{s}_2, \ldots, \boldsymbol{s}_N =: [\boldsymbol{s}_n]$ are modulated (pointwise multiplied)…
We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that…
Blind image restoration (IR) is a common yet challenging problem in computer vision. Classical model-based methods and recent deep learning (DL)-based methods represent two different methodologies for this problem, each with their own…
Let us consider the deconvolution problem, that is, to recover a latent source $x(\cdot)$ from the observations $\mathbf{y} = [y_1,\ldots,y_N]$ of a convolution process $y = x\star h + \eta$, where $\eta$ is an additive noise, the…