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Soft Computing
Published in: Soft Computing 5/2012

01-05-2012 | Focus

Towards interval-based non-additive deconvolution in signal processing

Authors: Olivier Strauss, Agnès Rico

Published in: Soft Computing | Issue 5/2012

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Abstract

Reconstructing a signal from its observations via a sensor device is usually called “deconvolution”. Such reconstruction requires perfect knowledge of the impulse response of the sensor involved in the signal measurement. The lower this knowledge, the more biased the reconstruction. In this paper, we present a novel method for reconstructing a signal measured by a sensor whose impulse response is imprecisely known. This technique is based on modeling the relationship between the measurement and the signal via a concave capacity and extending the convolution concept to a concave set of impulse responses. The reconstructed signal is interval-valued, thus reflecting the poor knowledge of the sensor impulse response.
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Footnotes
1
The conventional \(\bar{\nu}\) notation will not be used in this paper so as to make the equations below more easily understandable.
 
2
In Schmeidler (1989) the core is defined for a convex capacity. Our definition coincides with the definition proposed in Denneberg (1994) considering its conjugate (concave) capacity.
 
3
With \([{\bf x}] = [\underline {x}, \overline{x}]\) being a real interval, its radius is defined by \(rad([{\bf x}]) =\frac{1}{2}(\overline{x}-\underline {x}).\)
 
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Metadata
Title
Towards interval-based non-additive deconvolution in signal processing
Authors
Olivier Strauss
Agnès Rico
Publication date
01-05-2012
Publisher
Springer-Verlag
Published in
Soft Computing / Issue 5/2012
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-011-0771-7

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