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115
Image sampling below the nyquist density without aliasing
 J. Opt. Soc. Amer. A
, 1990
"... For multidimensional bandlimited functions, the Nyquist density is defined as that density corresponding to maximally packed spectral replications. Because of the shape of the support of the spectrum, however, sampling multidimensional functions at Nyquist densities can leave gaps among these repli ..."
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Cited by 17 (0 self)
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For multidimensional bandlimited functions, the Nyquist density is defined as that density corresponding to maximally packed spectral replications. Because of the shape of the support of the spectrum, however, sampling multidimensional functions at Nyquist densities can leave gaps among
Multidimensionalsignal sample dependency at Nyquist densities
, 1984
"... When a multidimensional signal is uniformly sampled, its spectrum is replicated. If the signal is band limited and the replications (1) contain regions that are identically zero and (2) are not aliased, then the samples are dependent. Indeed, lost samples can be regained from those remaining. In dim ..."
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. In dimensions greater than one, there are spectral regions of support for which this is the case even when sampling is performed at the Nyquist (minimum) density (e.g., a circular spectral region of support in two dimensions). When the known samples are perturbed by additive noise, lostsample restoration noise
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 1441 (15 self)
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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
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 696 (62 self)
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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
Constrained Capacities for FasterthanNyquist Signaling
"... This paper deals with capacity computations of fasterthanNyquist (FTN) signaling. It shows that the capacity of FTN is higher than the orthogonal pulse linear modulation capacity for all pulse shapes except the sinc. FTN signals can in fact achieve the ultimate capacity for the signal power spectr ..."
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Cited by 7 (3 self)
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This paper deals with capacity computations of fasterthanNyquist (FTN) signaling. It shows that the capacity of FTN is higher than the orthogonal pulse linear modulation capacity for all pulse shapes except the sinc. FTN signals can in fact achieve the ultimate capacity for the signal power
Density, overcompleteness, and localization of frames
 I. THEORY, J. FOURIER ANAL. APPL
, 2005
"... This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in ..."
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Cited by 62 (20 self)
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implications for irregular Gabor frames. Various Nyquist density results for Gabor frames are recovered as special cases, but in the process both their meaning and implications are clarified. New results are obtained on the excess and overcompleteness of Gabor frames, on the relationship between frame bounds
1SubNyquist Sampling: Bridging Theory and Practice
"... [ A review of past and recent strategies for subNyquist sampling] Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely ..."
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[ A review of past and recent strategies for subNyquist sampling] Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely
1SubNyquist Radar via Doppler Focusing
"... Abstract—We investigate the problem of a monostatic pulseDoppler radar transceiver trying to detect targets, sparsely populated in the radar’s unambiguous timefrequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample ra ..."
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rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here we describe a subNyquist sampling and recovery approach called Doppler focusing which addresses all of these problems: it performs low
ON GLOBAL COSTS AND NYQUIST'S THEOREM IN RANDOM VARIATE GENERATION
, 1989
"... We consider a large class of densities defined in terms of smoothness and tail conditions. Assume that we want to generate n iid random variables from a given density f in this class, and that the global cost of the generator is equal to the total number of evaluations of f We demonstrate with the h ..."
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function of bounded support and k th moment bounded by a given constant. In the last example, we proceed to show how Nyquist's theorem can be exploited to yield a generator with O(nl/(kI » expected cost. 1. Global cost. We consider a]arge class of densities defined in terms of smoothness and tail
Results 1  10
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115