Random Filters for Compressive Sampling and Reconstruction

By Joel A. Tropp, Michael B. Wakin, Marco F. Duarte, Dror Baron, Richard Baraniuk. 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, 2006

317 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d5e14f4d7916bc54cef6c5ae861707c2750cdd44

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In Biomedical Engineering

In Computational Mechanics

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Citations in the corpus

Compressive mechanism: utilizing sparse representation in differential privacy (2011, unknown): “2 Compressive Sensing Compressive sensing was introduced by [9, 11, 17], and later shown to have extensive applications in imaging [41, 33, 6], signal processing [44], computational biology [42], geophysical data analysis”
Signal Processing With Compressive Measurements (2010, unknown): “We start with the simple case where we desire a -stable embedding of , where and are ﬁnite sets of points in .”
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors (2011, background): “Several hardware inspired designs with only a few randomized components have also been shown to satisfy this property [3, 17–19].”
Compressive sensing: From theory to applications, a survey (2013, methodology): “Random filtering utilized in AIC requires less storage and computation for measurement and reconstruction [82].”
Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals (2007, result): “Although our interest is mainly in signalsx(t) ∈ M, our results are applicable to a broader class of signals, as explained in the relevant sections.”
Compressive Sensing by Random Convolution (2009, unknown): “By conjugate symmetry, we can rewrite this as a sum of vectors in RS , rk = σ1g1 + σn/2+1(−1)k−1gn/2+1 + 2 n/2∑ ω=2 Re [Fk,ωσ∗ωgω] (note that g1 and gn/2+1 will be real-valued).”
Toeplitz Compressed Sensing Matrices With Applications to Sparse Channel Estimation (2010, methodology): “In the compressed sensing literature, the first work to propose Toeplitz-structured observation matrices was [33], where observations were obtained by convolving the incoming unknown signal with a random filter—a filter whose taps were generated as realizations of certain random variables—followed b”
Fixed-Point Continuation for l1-Minimization: Methodology and Convergence (2008, background): “Applications of compressed sensing include compressive imaging [56, 65, 66], medical imaging [42], multisensor and distributed compressed sensing [1], analog-to-information conversion [36, 37, 38, 59], and missing data recovery [67].”
Random Projections of Smooth Manifolds (2009, background): “The computational complexity of applying an arbitrary M × N operator Φ is O(MN) per data point, though this complexity can be reduced through a careful, pseudorandom design of Φ [39].”
Toeplitz-Structured Compressed Sensing Matrices (2007, result): “It is also interesting to note that somewhat similar numerical results (without any performance guarantees) have been reported in [10] in the context of randomfilters.”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, unknown): “[22], in 2006.”
Compressive Sensing with structured random matrices (2012, methodology): “This setting was studied numerically in [132] by J.”
Block Compressed Sensing of Natural Images (2007, background): “In the special case when nB = 1, the proposed system boils down to the random filter system proposed in [5].”
Compressive Radar Imaging (2007, methodology): “Second, time-translated and frequency-modulated versions of the PN or chirp signals transmitted as radar waveforms sT (t) form a dictionary (the extension of a basis or frame) that is incoherent with the time, frequency, and time-frequency bases that sparsify or compress the above mentioned classes ”