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DOI: 10.4230/OASIcs.ICCSW.2013.3

A swarm based heuristic for sparse image recovery

Authors: Theofanis Apostolopoulos

Published in: OASIcs, Volume 35, 2013 Imperial College Computing Student Workshop

Abstract

This paper discusses the Compressive Sampling framework as an application for sparse representation (factorization) and recovery of images over an over-complete basis (dictionary). Compressive Sampling is a novel new area which asserts that one can recover images of interest, with much fewer measurements than were originally thought necessary, by searching for the sparsest representation of an image over an over-complete dictionary. This task is achieved by optimizing an objective function that includes two terms: one that measures the image reconstruction error and another that measures the sparsity level. We present and discuss a new swarm based heuristic for sparse image approximation using the Discrete Fourier Transform to enhance its level of sparsity. Our experimental results on reference images demonstrate the good performance of the proposed heuristic over other standard sparse recovery methods (L1-Magic and FOCUSS packages), in a noiseless environment using much fewer measurements. Finally, we discuss possible extensions of the heuristic in noisy environments and weakly sparse images as a realistic improvement with much higher applicability.

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Theofanis Apostolopoulos. A swarm based heuristic for sparse image recovery. In 2013 Imperial College Computing Student Workshop. Open Access Series in Informatics (OASIcs), Volume 35, pp. 3-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{apostolopoulos:OASIcs.ICCSW.2013.3,
  author =	{Apostolopoulos, Theofanis},
  title =	{{A swarm based heuristic for sparse image recovery}},
  booktitle =	{2013 Imperial College Computing Student Workshop},
  pages =	{3--10},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-63-7},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{35},
  editor =	{Jones, Andrew V. and Ng, Nicholas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICCSW.2013.3},
  URN =		{urn:nbn:de:0030-drops-42655},
  doi =		{10.4230/OASIcs.ICCSW.2013.3},
  annote =	{Keywords: Compressive Sampling, sparse image recovery, non-linear programming, sparse repre sentation, linear inverse problems}
}

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DOI: 10.4230/OASIcs.ICCSW.2012.8

A heuristic for sparse signal reconstruction

Authors: Theofanis Apostolopoulos

Published in: OASIcs, Volume 28, 2012 Imperial College Computing Student Workshop

Abstract

Compressive Sampling (CS) is a new method of signal acquisition and reconstruction from frequency data which do not follow the basic principle of the Nyquist-Shannon sampling theory. This new method allows reconstruction of the signal from substantially fewer measurements than those required by conventional sampling methods. We present and discuss a new, swarm based, technique for representing and reconstructing signals, with real values, in a noiseless environment. The method consists of finding an approximation of the l_0-norm based problem, as a combinatorial optimization problem for signal reconstruction. We also present and discuss some experimental results which compare the accuracy and the running time of our heuristic to the IHT and IRLS methods.

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Theofanis Apostolopoulos. A heuristic for sparse signal reconstruction. In 2012 Imperial College Computing Student Workshop. Open Access Series in Informatics (OASIcs), Volume 28, pp. 8-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{apostolopoulos:OASIcs.ICCSW.2012.8,
  author =	{Apostolopoulos, Theofanis},
  title =	{{A heuristic for sparse signal reconstruction}},
  booktitle =	{2012 Imperial College Computing Student Workshop},
  pages =	{8--14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-48-4},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{28},
  editor =	{Jones, Andrew V.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICCSW.2012.8},
  URN =		{urn:nbn:de:0030-drops-37589},
  doi =		{10.4230/OASIcs.ICCSW.2012.8},
  annote =	{Keywords: Compressive Sampling, sparse signal representation, l\underline0 minimisation, non-linear programming, signal recovery}
}

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A swarm based heuristic for sparse image recovery

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A heuristic for sparse signal reconstruction

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