## Abstract

Optical systems used for image acquisition are usually not perfect and

leading to degraded images. A typical degradation is image blur. Building

perfect optics is not always possible due to physical limitations, cost,

size or weight. Therefore, there is interest in computational solutions to

remove these degradations. By knowing the sources of distortion it is

possible to remove them.

Image blur can be removed by deconvolution, however, the problem

which has to be solved is underdetermined. For solving these ill-posed

problems additional assumptions have to be considered. Recently, many

advances were made in the investigation of underdetermined systems of

equations [1] in cases where the solution can be sparsely encoded. The

sparseness constraint is used to select a plausible solution out of an innite

set of possible solutions. This method is applied to the deconvolution

problem.

Similar to other approaches to deconvolution based on sparse coding,

for speed and memory eciency we apply the fast Fourier transform and

the fast wavelet transform to model the convolution and provide a sparse

basis [2]. For the convolution, boundary areas are cut to avoid wrong

modelling due to the cyclic nature of the Fourier transform. By cutting

the boundary areas the system of equations becomes underdetermined.

We apply this approach to a pinhole camera setting. Using a simulated

pinhole camera, we look at the in

uence of sparseness and the robustness

to noise. First tests have also been made using a real pinhole camera.

leading to degraded images. A typical degradation is image blur. Building

perfect optics is not always possible due to physical limitations, cost,

size or weight. Therefore, there is interest in computational solutions to

remove these degradations. By knowing the sources of distortion it is

possible to remove them.

Image blur can be removed by deconvolution, however, the problem

which has to be solved is underdetermined. For solving these ill-posed

problems additional assumptions have to be considered. Recently, many

advances were made in the investigation of underdetermined systems of

equations [1] in cases where the solution can be sparsely encoded. The

sparseness constraint is used to select a plausible solution out of an innite

set of possible solutions. This method is applied to the deconvolution

problem.

Similar to other approaches to deconvolution based on sparse coding,

for speed and memory eciency we apply the fast Fourier transform and

the fast wavelet transform to model the convolution and provide a sparse

basis [2]. For the convolution, boundary areas are cut to avoid wrong

modelling due to the cyclic nature of the Fourier transform. By cutting

the boundary areas the system of equations becomes underdetermined.

We apply this approach to a pinhole camera setting. Using a simulated

pinhole camera, we look at the in

uence of sparseness and the robustness

to noise. First tests have also been made using a real pinhole camera.

Original language | English |
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Title of host publication | Workshop New Challenges in Neural Computation 2011 |

Editors | Barbara Hammer, Thomas Villmann |

Number of pages | 1 |

Volume | 05 |

Publication date | 16.08.2011 |

Pages | 9 - 9 |

Publication status | Published - 16.08.2011 |