Related papers: Polar Deconvolution of Mixed Signals
We propose a deconvolution algorithm for images blurred and degraded by a Poisson noise. The algorithm uses a fast proximal backward-forward splitting iteration. This iteration minimizes an energy which combines a \textit{non-linear} data…
Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies of a band-limited or diffraction-limited point…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perhaps using wavelet denoising, and then to apply a clustering…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
We consider the problem of demixing a sequence of source signals from the sum of noisy bilinear measurements. It is a generalized mathematical model for blind demixing with blind deconvolution, which is prevalent across the areas of…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
We investigate the problem of reconstructing signals from a subsampled convolution of their modulated versions and a known filter. The problem is studied as applies to specific imaging systems relying on spatial phase modulation by randomly…
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Many satellite communication systems operating today employ low cost upconverters or downconverters which create phase noise. This noise can severely limit the information rate of the system and pose a serious challenge for the detection…
We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…
The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…
This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding,…
A sharp phase transition emerges in convex programs when solving the linear inverse problem, which aims to recover a structured signal from its linear measurements. This paper studies this phenomenon in theory under Gaussian random…
This paper focuses on solving a challenging problem of blind deconvolution demixing involving modulated inputs. Specifically, multiple input signals $s_n(t)$, each bandlimited to $B$ Hz, are modulated with known random sequences $r_n(t)$…
In this paper, we incorporate a graph filter deconvolution step into the classical geometric convolutional neural network pipeline. More precisely, under the assumption that the graph domain plays a role in the generation of the observed…
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…
The development of signal unmixing algorithms is essential for leveraging multimodal datasets acquired through a wide array of scientific imaging technologies, including hyperspectral or time-resolved acquisitions. In experimental physics,…
We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear…