Improved bounds on Restricted isometry for compressed sensing

By Hiroshi Inoue, 井上寛, ヒロシイノウエ. 2013

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Citations in the corpus

Learning to learn by gradient descent by gradient descent (2016, background): “In contrast, communities who focus on sparsity tend to favor very different approaches [Donoho, 2006, Bach et al., 2012].”
Automated Machine Learning: From Principles to Practices (2018, background): “Autoencoder is a kind of artificial neural network used to learn efficient coding and the encoding space should possess useful properties.”
Using Non-invertible Data Transformations to Build Adversarial-Robust Neural Networks (2016, background): “However, since we speciﬁcally design C to be highly correlated, the upper bound will be signiﬁcantly larger than the lower bound [9], [6], and thus result in a larger range for the reconstruction error.”
Efficient and reliable low-power backscatter networks (2012, background): “In compressive sensing, estimating z′ is formulated as an optimization problem [13, 9]:”
Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates (2014, methodology): “Different algorithms have been developed to solve ðP0Þ or ðP0;dÞ in the active field of compressed sensing [26,27,46].”
Far-field super-resolution ghost imaging with a deep neural network constraint (2022, background): “However, it is still a challenging problem for GISC to operate well in the case when β is less than the Cramer – Rao bound 16,17,22 .”
The Convex Geometry of Linear Inverse Problems (2010, methodology): “This method has seen a surge in interest in the last few years as it provides a tractable convex optimization formulation to exactly recover sparse vectors under various conditions [16, 26, 27].”
Robust Compressed Sensing MRI with Deep Generative Priors (2021, background): “2 Related Work Generative priors have shown great utility to improving compressed sensing and other inverse problems, starting with [13], who generalized the theoretical framework of compressed sensing and restricted eigenvalue conditions [81, 23, 12, 15, 39, 11, 10, 25] for signals lying on the ran”
Gadgetron: An open source framework for medical image reconstruction (2013, background): “Examples include parallel MRI reconstruction (1–3) and more recently compressive sensing (4,5).”
Design and Analysis of a Hardware-Efficient Compressed Sensing Architecture for Data Compression in Wireless Sensors (2012, background): “For a more theoretical and thorough background on compressed sensing, please refer to [9], [11], [15].”
Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems (2017, background): “Compressed sensing theory [19, 14] has further extended the idea to demonstrate that an accurate recovery is possible from undersampled data, if the signal is sparse in some frames and the sensing matrix is incoherent.”
Deep Residual Learning for Accelerated MRI Using Magnitude and Phase Networks (2018, background): “Wang et al [19] applied deep learning to CS-MRI, training the CNN from down-sampled reconstruction images to learn fully sampled reconstruction.”
Channel Estimation via Orthogonal Matching Pursuit for Hybrid MIMO Systems in Millimeter Wave Communications (2016, methodology): “1 The pilot overhead of the CS-based methods is given by O (L ln NT), where L is the number of non-zero spatial channel paths (or the sparsity level) and NT is the number of transmit antennas [16], [17].”
Statistical Mechanics of Optimal Convex Inference in High Dimensions (2016, background): “Remarkable advances in measurement technologies have thrust us squarely into the modern age of “bigdata,” which yields the potential to revolutionize a variety of fields spanning the sciences, engineering, and humanities, including neuroscience [1, 2], systems biology [3], health care [4], economics”
Oracle inequalities in empirical risk minimization and sparse recovery problems (2011, background): “, Donoho [35, 36, 37, 39], Candes and Tao [29], Rudelson and Vershynin [82], Mendelson, Pajor and Tomczak-Jaegermann [78], Bunea, Tsybakov and Wegkamp [25], van de Geer [46], Koltchinskii [64, 65, 66], Bickel, Ritov and Tsybakov [14] among many other papers that study both the random design and the ”
Cell-Free Massive MIMO: A New Next-Generation Paradigm (2019, background): “sensing [50] may be readily invoked for exploiting this sparsity.”