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Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems

Abstract: 

Sampling and reconstruction of bandlimited graph signals have well-appreciated merits for dimensionality reduction, affordable storage, and online processing of streaming network data. However, these parsimonious signals are oftentimes encountered with high-dimensional linear inverse problems. Hence, interest shifts from reconstructing the signal itself towards instead approximating the input to a prescribed linear operator efficiently. In this context, we propose a novel sampling scheme that leverages the bandlimitedness of the output as well as the transformation whose input we wish to approximate. We formulate problems to jointly optimize sample selection and a sketch of the target inverse mapping, so when the latter is affordably applied to the sampled output signal, the result is close to the desired input. The developed sampling plus reduced-complexity processing pipeline is particularly useful for streaming data, where the linear transform has to be applied fast and repeatedly to successive response signals.

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Paper Details

Authors:
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro
Submitted On:
8 December 2016 - 12:32am
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Fernando Gama
Paper Code:
SPN-4.4
Document Year:
2016
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Document Files

sketching-globalsip16-presentation.pdf

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[1] Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro, "Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1420. Accessed: May. 25, 2017.
@article{1420-16,
url = {http://sigport.org/1420},
author = {Fernando Gama; Antonio G. Marques; Gonzalo Mateos; Alejandro Ribeiro },
publisher = {IEEE SigPort},
title = {Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems},
year = {2016} }
TY - EJOUR
T1 - Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems
AU - Fernando Gama; Antonio G. Marques; Gonzalo Mateos; Alejandro Ribeiro
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1420
ER -
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. (2016). Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems. IEEE SigPort. http://sigport.org/1420
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro, 2016. Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems. Available at: http://sigport.org/1420.
Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. (2016). "Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems." Web.
1. Fernando Gama, Antonio G. Marques, Gonzalo Mateos, Alejandro Ribeiro. Rethinking Sketching as Sampling: Efficient Approximate Solution to Linear Inverse Problems [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1420