10 accepted papers
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios, the graph may not be accurately known, and there may exist…
Compressed sensing, which involves reconstruction of sparse signals from an under-determined linear system, has been recently applied to problems in group testing to save on the number of tests administered during a pandemic or other resource-constrained scenarios. In practical group testing in time…
This study presents a technique for 2D tomography under unknown viewing angles when the distribution of the viewing angles is also unknown. Unknown view tomography (UVT) is a problem encountered in cryo-electron microscopy and in the geometric calibration of CT systems. There exists a moderate-sized…
In this study, we consider a variant of unlabelled sensing where the measurements are sparsely permuted, and additionally, a few correspondences are known. We present an estimator to solve for the unknown vector. We derive a theoretical upper bound on the ℓ<inf xmlns:mml="http://www.w3.org/1998/Math…
Compressed Sensing assumes a linear model for acquiring signals however imperfections may arise in the specification of the ‘ideal’ measurement model. We present the first study which considers the case of two such common calibration issues: (a) unknown measurement scaling (sensor gains) due to hard…
Group testing can save testing resources in the context of the ongoing COVID-19 pandemic. In group testing, we are given n samples, one per individual, and arrange them into m < n pooled samples, where each pool is obtained by mixing a subset of the n individual samples. Infected individuals are the…
Images of static scenes submerged beneath a wavy water surface exhibit severe non-rigid distortions. The physics of water flow suggests that water surfaces possess spatio-temporal smoothness and temporal periodicity. Hence they possess a sparse representation in the 3D discrete Fourier (DFT) basis.…
The analysis of reconstruction errors for compressed sensing under Poisson noise is challenging due to the signal dependent nature of the noise, and also because the Poisson negative log-likelihood is not a metric. In this paper, we present error bounds for reconstruction of signals which are sparse…
This paper presents a method for improving the recovery guarantee for signals that are sparse or compressible in some general basis (dictionary) using a splitting and reordering approach. The splitting algorithm applies existing results for dictionaries that are naturally characterized as a concaten…
Imaging techniques involve counting of photons striking a detector. Due to fluctuations in the counting process, the measured photon counts are known to be corrupted by Poisson noise. In this paper, we propose a blind dictionary learning framework for the reconstruction of photographic image data fr…