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Compressive sampling
, 2006
"... Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired res ..."
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Cited by 1427 (15 self)
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resolution of the image, i.e. the number of pixels in the image. This paper surveys an emerging theory which goes by the name of “compressive sampling” or “compressed sensing,” and which says that this conventional wisdom is inaccurate. Perhaps surprisingly, it is possible to reconstruct images or signals
Sparsity and Incoherence in Compressive Sampling
, 2006
"... We consider the problem of reconstructing a sparse signal x 0 ∈ R n from a limited number of linear measurements. Given m randomly selected samples of Ux 0, where U is an orthonormal matrix, we show that ℓ1 minimization recovers x 0 exactly when the number of measurements exceeds m ≥ Const · µ 2 (U) ..."
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Cited by 237 (14 self)
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We consider the problem of reconstructing a sparse signal x 0 ∈ R n from a limited number of linear measurements. Given m randomly selected samples of Ux 0, where U is an orthonormal matrix, we show that ℓ1 minimization recovers x 0 exactly when the number of measurements exceeds m ≥ Const · µ 2 (U
Singlepixel imaging via compressive sampling
 IEEE Signal Processing Magazine
"... Humans are visual animals, and imaging sensors that extend our reach – cameras – have improved dramatically in recent times thanks to the introduction of CCD and CMOS digital technology. Consumer digital cameras in the megapixel range are now ubiquitous thanks to the happy coincidence that the semi ..."
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Cited by 298 (20 self)
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fuses a new camera architecture based on a digital micromirror device (DMD – see Sidebar: Spatial Light Modulators) with the new mathematical theory and algorithms of compressive sampling (CS – see Sidebar: Compressive Sampling in a Nutshell). CS combines sampling and compression into a single
Backgrounds What is Compressive Sampling? Compressive Sampling is a
"... This project aims to investigate whether Compressive Sampling can be utilized to reduce the data acquisition time for Terahertz time domain spectroscopy (THzTDS). ..."
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This project aims to investigate whether Compressive Sampling can be utilized to reduce the data acquisition time for Terahertz time domain spectroscopy (THzTDS).
Compressive sampling for signal classification
 in Proc. 40th Asilomar Conf. Signals, Systems and Computers
, 2006
"... Compressive Sampling (CS), also called Compressed Sensing, entails making observations of an unknown signal by projecting it onto random vectors. Recent theoretical results show that if the signal is sparse (or nearly sparse) in some basis, then with high probability such observations essentially en ..."
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Cited by 36 (2 self)
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Compressive Sampling (CS), also called Compressed Sensing, entails making observations of an unknown signal by projecting it onto random vectors. Recent theoretical results show that if the signal is sparse (or nearly sparse) in some basis, then with high probability such observations essentially
Compressive Sampling for Signal Detection
 In Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing (ICASSP
, 2007
"... Compressive sampling (CS) refers to a generalized sampling paradigm in which observations are inner products between an unknown signal vector and userspecified test vectors. Among the attractive features of CS is the ability to reconstruct any sparse (or nearly sparse) signal from a relatively sm ..."
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Cited by 43 (1 self)
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Compressive sampling (CS) refers to a generalized sampling paradigm in which observations are inner products between an unknown signal vector and userspecified test vectors. Among the attractive features of CS is the ability to reconstruct any sparse (or nearly sparse) signal from a relatively
Combined Compressive Sampling and Image
"... Abstract A procedure for image watermarking in the presence of compressive sampling is proposed. The randomly chosen measurements from image blocks are used to carry the watermark. The image reconstruction based on a set of watermarked measurements is performed using the total variation minimizatio ..."
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Abstract A procedure for image watermarking in the presence of compressive sampling is proposed. The randomly chosen measurements from image blocks are used to carry the watermark. The image reconstruction based on a set of watermarked measurements is performed using the total variation
THE COMPRESSEDSAMPLING FILTER (CSF)
"... Abstract—The common approaches to sample a signal generally follow the wellknown NyquistShannon’s theorem: the sampling rate must be at least twice the maximum frequency presented in the signal. A new emerging field, compressed sampling (CS), has made a paradigmatic step to sample a signal with mu ..."
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Abstract—The common approaches to sample a signal generally follow the wellknown NyquistShannon’s theorem: the sampling rate must be at least twice the maximum frequency presented in the signal. A new emerging field, compressed sampling (CS), has made a paradigmatic step to sample a signal
Compressive sensing
 IEEE Signal Processing Mag
, 2007
"... The Shannon/Nyquist sampling theorem tells us that in order to not lose information when uniformly sampling a signal we must sample at least two times faster than its bandwidth. In many applications, including digital image and video cameras, the Nyquist rate can be so high that we end up with too m ..."
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Cited by 687 (65 self)
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many samples and must compress in order to store or transmit them. In other applications, including imaging systems (medical scanners, radars) and highspeed analogtodigital converters, increasing the sampling rate or density beyond the current stateoftheart is very expensive. In this lecture, we
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