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Sampling and recovery of pulse streams.

Hegde, Chinmay.

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Sampling and recovery of pulse streams.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Sampling and recovery of pulse streams./
作者:	Hegde, Chinmay.
面頁冊數:	54 p.
附註:	Source: Masters Abstracts International, Volume: 49-01, page: 0575.
Contained By:	Masters Abstracts International49-01.
標題:	Engineering, Computer. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1486067
ISBN:	9781124212845

Sampling and recovery of pulse streams.
Hegde, Chinmay.

Sampling and recovery of pulse streams. - 54 p.

Source: Masters Abstracts International, Volume: 49-01, page: 0575.

Thesis (M.S.)--Rice University, 2010.

Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N -dimensional basis representation has just K << N significant coefficients; in this case, the CS theory maintains that just M = O (K log N) random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K = SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K = SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS.

ISBN: 9781124212845Subjects--Topical Terms:

1669061
Engineering, Computer.

Sampling and recovery of pulse streams.
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502 $a Thesis (M.S.)--Rice University, 2010.
520 $a Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N -dimensional basis representation has just K << N significant coefficients; in this case, the CS theory maintains that just M = O (K log N) random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K = SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K = SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS.
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