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The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used…
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist…
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying…
Compressed Sensing MRI (CS-MRI) aims at reconstructing de-aliased images from sub-Nyquist sampling k-space data to accelerate MR Imaging, thus presenting two basic issues, i.e., where to sample and how to reconstruct. To deal with both…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
Multispectral photoacoustic tomography (PAT) is an imaging modality that utilizes the photoacoustic effect to achieve non-invasive and high-contrast imaging of internal tissues. However, the hardware cost and computational demand of a…
Implicit Neural Representations (INR) have been successfully employed for Arbitrary-scale Super-Resolution (ASR). However, INR-based models need to query the multi-layer perceptron module numerous times and render a pixel in each query,…
In non-linear estimations, it is common to assess sampling uncertainty by bootstrap inference. For complex models, this can be computationally intensive. This paper combines optimization with resampling: turning stochastic optimization into…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
We investigate super-resolution methods for image reconstruction from data provided by a family of scanning instruments like the Herschel observatory. To do this, we constructed a model of the instrument that faithfully reflects the…
Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed in high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model,…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However,…
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…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
Large-scale astronomical surveys can capture numerous images of celestial objects, including galaxies and nebulae. Analysing and processing these images can reveal intricate internal structures of these objects, allowing researchers to…