Compressed sensing in MRI enables high subsampling factors while maintaining diagnostic image quality. This technique enables shortened scan durations and/or improved image resolution. Further, compressed sensing can increase the diagnostic information and value from each scan performed. Overall, compressed sensing has…
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48 results for “Compressive sensing”
This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible signal-to-noise-ratio (SNR) levels, improving on previous work in adaptive comp…
As a lossy compression framework, compressed sensing has drawn much attention in wireless telemonitoring of biosignals due to its ability to reduce energy consumption and make possible the design of low-power devices. However, the non-sparseness of biosignals presents a major challenge to compressed sensing. This study…
Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priorscs.LG
Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.
problem Accurately recovering vectors from 1-bit measurements using structured matrices.
method Correlation-based optimization with randomly signed partial Gaussian circulant matrices and generative models.
result Recovery guarantees match those for i.i.d. Gaussian matrices but with faster computation.
We provide a comprehensive review of classical algorithms for compressive sensing of images, focused on Total variation methods, with a view to application in LiDAR systems. Our primary focus is providing a full review for beginners in the field, as well as simulating the kind of noise found in real LiDAR systems. To t…
New algorithm speeds up cluster-based compressive sensing tasks.
problem Efficiently solving multiple compressive sensing tasks with shared information.
method Combines Monte Carlo sampling with iterative linear solvers to avoid explicit covariance matrix computation.
result Up to thousands of times faster and orders of magnitude more memory-efficient compared to existing methods.
This letter proposes a sparse diffusion steepest-descent algorithm for one bit compressed sensing in wireless sensor networks. The approach exploits the diffusion strategy from distributed learning in the one bit compressed sensing framework. To estimate a common sparse vector cooperatively from only the sign of measur…
Proposes using equivariant generative models for compressed sensing with unknown orientations.
problem Recovering signals with unknown orientations from underdetermined systems of linear measurements.
method Equivariant variational autoencoder as a generative prior for compressed sensing.
result Signals with unknown orientations can be recovered using iterative gradient descent on the latent space of equivariant models.
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised representation learning inspired by compressed sensing. We treat the low-dimensional …
Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Financestat.ML
CSDM integrates compressed sensing into diffusion models for faster data generation.
problem Efficiently generating synthetic data in high-dimensional spaces.
method Integrating compressed sensing into diffusion models (CSDM) to reduce dimensionality and accelerate inference.
result Achieves provably faster convergence and better latent space dimension selection.
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L0 norm and Schatten-0 norm is proposed to enforce cosparsity and low r…
New method uses generative priors for compressive sensing with sparse solutions.
problem Fundamental linear inverse problem in compressive sensing.
method Sparse Bayesian learning with conditional Gaussianity.
result Ability to learn from few compressed and noisy samples without optimization.
Improves convergence speed in compressive sensing with a new probabilistic approach.
problem Efficiently solving the best subset selection problem in compressive sensing.
method Smooth probabilistic reformulation of regularized regression.
result Empirically outperforms existing compressive sensing algorithms across various settings.
The paper provides theoretical guarantees for optimized sampling in compressed sensing, showing error vanishes with more measurements.
problem Theoretical and practical improvements in compressed sensing with optimized sampling schemes.
method Theoretical analysis and empirical experiments with optimized sampling schemes for subsampled unitary matrices.
result The error caused by measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming Gaussian noise.
Optimized sampling scheme for compressed sensing combining randomness and determinism.
problem Improving compressed sensing performance with deterministic sampling.
method Optimized sampling scheme combining random and deterministic selection of rows.
result Measurable improvements in image compressed sensing for generative and sparse priors.
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the ou…
The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector. Motivated by recent advances in compressive sensing with generative models, where a generative modeling assumption replaces the u…
This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix $\Ab$ an…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guara…
AdaBoost improves binary classification in robust one-bit compressed sensing with adversarial errors.
problem Binary classification in robust one-bit compressed sensing with adversarial errors.
method AdaBoost and max--margin-classifier approach, with convergence rates improved under certain feature conditions.
result Improved convergence rates and explanation for harmless interpolating adversarial noise.
Video analytics requires operating with large amounts of data. Compressive sensing allows to reduce the number of measurements required to represent the video using the prior knowledge of sparsity of the original signal, but it imposes certain conditions on the design matrix. The Bayesian compressive sensing approach r…
Paper proposes robust compressed sensing using generative models.
problem Estimating high-dimensional vectors from noisy linear equations with heavy-tailed or outlier data.
method Inspired by Median-of-Means (MOM), proposes an algorithm for robust recovery.
result Guarantees recovery for heavy-tailed data, even in the presence of outliers.
A new deep learning framework for efficient IoT data compression and inference.
problem Limited bandwidth and power resources in IoT sensors.
method Co-designed deep learning framework that maximizes sensing goal accuracy.
result Superior performance compared to benchmark models.
We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for compressive sensing inversion based on convolutional factor analysis is develope…
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tr…
We present an information-theoretic framework for sequential adaptive compressed sensing, Info-Greedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is Info-Greedy for a family of -sparse signals b…
Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.
problem Signal recovery from generative priors in compressed sensing.
method Stochastic Gradient Langevin Dynamics (SGLD) for signal recovery.
result SGLD converges to the true signal under mild assumptions on the generative model.
New coherence parameter for GNNs with Fourier measurements improves signal recovery.
problem Characterizing generative compressed sensing with Fourier measurements.
method Subspace counting arguments and high-dimensional probability theory.
result First known restricted isometry guarantee for generative compressed sensing with subsampled isometries.
Unified approach for robust low rank matrix estimation with adversaries.
problem Robust low rank matrix estimation in the presence of adversaries.
method Unified approach combining Huber loss and nuclear norm penalization.
result Sharp estimation error bounds for matrix compressed sensing and completion.
Improved compressed sensing using a generator that learns from measurements.
problem Signal recovery accuracy in compressed sensing.
method Proposes a framework that uses measurement-conditional generative models to refine signal estimation.
result Uniformly superior performance with up to an order of magnitude reduction in reconstruction error.
Binary Iterative Hard Thresholding converges with optimal number of 1-bit measurements.
problem Recovering sparse signals from 1-bit compressed measurements.
method Binary Iterative Hard Thresholding (BIHT) algorithm.
result BIHT converges with only O(k/ε) measurements, optimal for recovery.
Machine learning at the edge offers great benefits such as increased privacy and security, low latency, and more autonomy. However, a major challenge is that many devices, in particular edge devices, have very limited memory, weak processors, and scarce energy supply. We propose a hybrid hardware-software framework tha…
In this work, we consider compressed sensing reconstruction from measurements of -sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine, can be trained in an unsupervised manner on example signals, we demonstrate how…
Paper quantizes heavy-tailed data for near optimal estimation rates.
problem Estimating parameters from heavy-tailed data with quantization.
method Truncate and dither data, then uniformly quantize; achieves near minimax rates.
result Near optimal estimation rates achievable with quantized data.
This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypot…
Compressed Factorization: Fast and Accurate Low-Rank Factorization of Compressively-Sensed Datacs.LG
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections. We examine the approach of first performing factorization in the compressed dom…
Paper develops a decoder for sparse codes without encoder matrix, achieving optimal recovery.
problem Designing a decoder for sparse codes from linear measurements alone.
method Matrix factorization to recover encoder and sparse coding matrices from measurements.
result Decoder-Expander Based Factorisation recovers encoder and sparse coding matrix at optimal measurement rate with high probability.
Paper proposes a new binary quantization method for faster DNN inference.
problem Accelerating deep neural network inference on resource-limited devices.
method Quantized Compressed Sensing (QCS) for binary quantization.
result The proposed method preserves benefits of standard methods while reducing quantization error.
Compressed imitation learning uses simplicity priors for efficient expert behavior copying.
problem Efficiently learn expert behaviors with minimal data.
method Utilizes policy simplicity as a prior for sample-efficient imitation learning.
result Significantly higher scores achieved with limited expert demonstrations.
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allo…
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a generative model. We search and constrain on latent variable space to make the m…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural …
We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by us…
In compressed sensing problems, minimization or Basis Pursuit was known to have the best provable phase transition performance of recoverable sparsity among polynomial-time algorithms. It is of great theoretical and practical interest to find alternative polynomial-time algorithms which perform better than $\e…
Paper tackles 1-bit compressed sensing, presenting efficient algorithm for sparse signal estimation.
problem Estimating sparse signals from binary measurements.
method Non-convex sparsity-constrained program with one-shot hard thresholding.
result Simple algorithm produces accurate signal approximation with high probability.
Algorithm estimates principal eigenvector with adaptive sensing, improving over non-adaptive methods.
problem Estimating principal eigenvector with limited scalar measurements.
method Compressed variant of Oja's algorithm using two adaptive measurements per sample.
result Convergence rate of after iterations, matching information-theoretic lower bound.
Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body-area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with…
Characterization of point-source transient events with a rolling-shutter compressed sensing systemstat.ML
A new compressed sensing system speeds up PSTE detection.
problem Accurately detecting fast, small optical events (PSTEs) is challenging.
method Developed a novel compressed sensing algorithm for rolling shutter systems.
result Accurately recovered PSTEs with spatial undersampling, showing speed and quality advantages.