scholarly journals Performance Bounds For Co-/Sparse Box Constrained Signal Recovery

2019 ◽  
Vol 27 (1) ◽  
pp. 79-106
Author(s):  
Jan Kuske ◽  
Stefania Petra
Keyword(s):  
Low Complexity ◽  
Signal Recovery ◽  
Performance Bounds ◽  
Linear Measurements ◽  
Complexity Measures ◽  
Rate Dependent ◽  
Intrinsic Complexity ◽  
Convex Regularization ◽  
Signal Image ◽  
Random Measurements

Abstract The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The CS theory shows that any signal/image can be undersampled at a rate dependent on its intrinsic complexity. Moreover, in such undersampling regimes, the signal can be recovered by sparsity promoting convex regularization like ℓ1- or total variation (TV-) minimization. Precise relations between many low complexity measures and the sufficient number of random measurements are known for many sparsity promoting norms. However, a precise estimate of the undersampling rate for the TV seminorm is still lacking. We address this issue by: a) providing dual certificates testing uniqueness of a given cosparse signal with bounded signal values, b) approximating the undersampling rates via the statistical dimension of the TV descent cone and c) showing empirically that the provided rates also hold for tomographic measurements.

scholarly journals Properties and Iterative Methods for theQ-Lasso

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Mohammad Ali Alghamdi ◽  
Naseer Shahzad ◽  
Hong-Kun Xu
Keyword(s):  
Iterative Methods ◽  
Convex Subset ◽  
Gradient Algorithm ◽  
Tuning Parameter ◽  
Linear Measurements ◽  
Tolerance Level ◽  
Basic Properties ◽  
Proximal Gradient Algorithm ◽  
Signal Image

We introduce theQ-lasso which generalizes the well-known lasso of Tibshirani (1996) withQa closed convex subset of a Euclideanm-space for some integerm≥1. This setQcan be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image via the lasso. Solutions of theQ-lasso depend on a tuning parameterγ. In this paper, we obtain basic properties of the solutions as a function ofγ. Because of ill posedness, we also applyl1-l2regularization to theQ-lasso. In addition, we discuss iterative methods for solving theQ-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm.

scholarly journals Difference of two norms-regularizations for Q-Lasso

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdellatif Moudafi
Keyword(s):  
Computational Effort ◽  
Gradient Algorithm ◽  
Signal Recovery ◽  
Cardinality Constraint ◽  
Linear Measurements ◽  
Dc Algorithm ◽  
Difference Of Convex Functions ◽  
Convergence Results ◽  
The Difference ◽  
New Algorithms

The focus of this paper is in Q-Lasso introduced in Alghamdi et al. (2013) which extended the Lasso by Tibshirani (1996). The closed convex subset Q belonging in a Euclidean m-space, for m∈IN, is the set of errors when linear measurements are taken to recover a signal/image via the Lasso. Based on a recent work by Wang (2013), we are interested in two new penalty methods for Q-Lasso relying on two types of difference of convex functions (DC for short) programming where the DC objective functions are the difference of l1 and lσq norms and the difference of l1 and lr norms with r>1. By means of a generalized q-term shrinkage operator upon the special structure of lσq norm, we design a proximal gradient algorithm for handling the DC l1−lσq model. Then, based on the majorization scheme, we develop a majorized penalty algorithm for the DC l1−lr model. The convergence results of our new algorithms are presented as well. We would like to emphasize that extensive simulation results in the case Q={b} show that these two new algorithms offer improved signal recovery performance and require reduced computational effort relative to state-of-the-art l1 and lp (p∈(0,1)) models, see Wang (2013). We also devise two DC Algorithms on the spirit of a paper where exact DC representation of the cardinality constraint is investigated and which also used the largest-q norm of lσq and presented numerical results that show the efficiency of our DC Algorithm in comparison with other methods using other penalty terms in the context of quadratic programing, see Jun-ya et al. (2017).

scholarly journals Uncovering biomarkers during therapeutic neuromodulation with PARRM: Period-based Artifact Reconstruction and Removal Method

2020 ◽  
Author(s):  
Evan M. Dastin-van Rijn ◽  
Nicole R. Provenza ◽  
Jonathan S. Calvert ◽  
Ro’ee Gilron ◽  
Anusha B. Allawala ◽  
...  
Keyword(s):  
Real Time ◽  
Low Complexity ◽  
Signal Recovery ◽  
Complex Signals ◽  
Artifact Removal ◽  
Neural Recordings ◽  
Removal Method ◽  
The Central Nervous System ◽  
Novel Method

AbstractAdvances in device development have enabled concurrent stimulation and recording at adjacent locations in the central nervous system. However, stimulation artifacts obscure the sensed underlying neural activity. Here, we developed a novel method, termed Period-based Artifact Reconstruction and Removal Method (PARRM), to remove stimulation artifacts from neural recordings by leveraging the exact period of stimulation to construct and subtract a high-fidelity template of the artifact. Benchtop saline experiments, computational simulations, five unique in vivo paradigms across animal and human studies, and an obscured movement biomarker were used for validation. Performance was found to exceed that of state-of-the-art filters in recovering complex signals without introducing contamination. PARRM has several advantages: it is 1) superior in signal recovery; 2) easily adaptable to several neurostimulation paradigms; and 3) low-complexity for future on-device implementation. Real-time artifact removal via PARRM will enable unbiased exploration and detection of neural biomarkers to enhance efficacy of closed-loop therapies.SummaryOnline, real-time artifact removal via PARRM will enable unbiased exploration of neural biomarkers previously obscured by stimulation artifact.

scholarly journals Application of Information and Complexity Measures to Neutron Stars Structure

2019 ◽  
Vol 18 ◽  
pp. 163
Author(s):  
K. Ch. Chatzisavvas ◽  
V. P. Psonis ◽  
C. P. Panos ◽  
Ch. C. Moustakidis
Keyword(s):  
Gravitational Field ◽  
Neutron Star ◽  
Neutron Stars ◽  
Short Range ◽  
Nuclear Force ◽  
Low Complexity ◽  
Complexity Measures ◽  
Astronomical Observations ◽  
Equation Of States ◽  
Statistical Complexity

We apply several information and statistical complexity measures to neutron stars structure. Neutron stars is a classical example where the gravitational field and quantum behaviour are combined and produce a macroscopic dense object. We concentrate our study on the connection between complexity and neutron star properties, like maximum mass and the corresponding radius, applying a specific set of realistic equation of states. Moreover, the effect of the strength of the gravitational field on the neutron star structure and consequently on the complexity measure is also investigated. It is seen that neutron stars, consistent with astronomical observations so far, are ordered systems (low complexity), which cannot grow in complexity as their mass increases. This is a result of the interplay of gravity, the short-range nuclear force and the very short-range weak interaction.

scholarly journals Cyber-Physical Systems: An Information-Theoretic Framework for Joint CS-ICA Recovery of Sparse Source Biosignals.

2020 ◽  
Author(s):  
Yahia Alghorani ◽  
salama Ikki
Keyword(s):  
Adaptive Design ◽  
Algorithm Design ◽  
Vital Signs ◽  
Low Complexity ◽  
Cyber Physical Systems ◽  
Signal Recovery ◽  
Digital To Analog Converter ◽  
Information Theoretic ◽  
Physical Systems ◽  
Recovery Algorithms

<div>The aim of this study is to propose an information-theoretic</div><div>framework that can be used for joint recovery of sparse</div><div>source biosignals. The proposed method supports medical cyber-physical systems (CPS) that enhance the detection, tracking, and monitoring of vital signs via wearable biosensors. Specifically, we address the problem of sparse signal recovery and acquisition in wearable biosensor networks, where we develop an adaptive design methodology based on compressed sensing (CS) and</div><div>independent component analysis (ICA) to reduce and eliminate artifacts and interference in sparse biosignals. Our analysis and examples offer a low-complexity algorithm design for patient monitoring systems, where sparse source biosignals can be recovered at low hardware costs and power consumption. Also, we show that, under noisy measurement conditions, the joint CS-ICA recovery algorithms can outperform standard CS methods, where a sparse biosignal is retrieved in a few measurement. By implementing the joint sparse recovery algorithms, the error in reconstructing sparse biosignals is reduced, and a digital-to-analog converter operates at low-speed and low-resolution.</div>

scholarly journals A Low-Complexity Biosignal Recovery Algorithm using Compressed Sensing and Independent Component Analysis

2020 ◽  
Author(s):  
Yahia Alghorani ◽  
salama Ikki
Keyword(s):  
Independent Component Analysis ◽  
Compressed Sensing ◽  
Low Cost ◽  
Vital Signs ◽  
Low Complexity ◽  
Component Analysis ◽  
Independent Component ◽  
Signal Recovery ◽  
Recovery Algorithm ◽  
Ica Algorithm

<div>The aim of this study is to propose a low-complexity algorithm that can be used for the joint sparse recovery of biosignals. The framework of the proposed algorithm supports real-time patient monitoring systems that enhance the detection, tracking, and monitoring of vital signs via wearable biosensors. Specifically, we address the problem of sparse signal recovery and acquisition in wearable biosensor networks, where we develop an efficient computational framework using compressed sensing (CS) and independent component analysis (ICA) to reduce and eliminate artifacts and interference in sparse biosignals. Our analysis and examples indicate that the CS-ICA algorithm helps to develop low-cost, low-power wearable biosensors while improving data quality and accuracy for a given measurement. We also show that, under noisy measurement conditions, the CS-ICA algorithm can outperform the standard CS method, where a biosignal can be retrieved in only a few measurements. By implementing the sensing framework, the error in reconstructing biosignals is reduced, and a digital-to-analog converter operates at low-speed and low-resolution</div>

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