Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling and Recovery of Pulse Streams   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 = 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.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: stat