Relationship between the robust statistics theory and sparse compressive sensed signals reconstruction

Srdjan Stanković; Ljubisa Stanković; Irena Orović

Relationship between the robust statistics theory and sparse compressive sensed signals reconstruction

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Author(s): Srdjan Stanković ¹ ; Ljubisa Stanković ¹ ; Irena Orović ¹
- Affiliations: 1: University of Montenegro; Faculty of Electrical Engineering, Džordža Vašingtona bb, 81000 Podgorica, Montenegro
Source: Volume 8, Issue 3, May 2014, p. 223 – 229
DOI: 10.1049/iet-spr.2013.0348 , Print ISSN 1751-9675, Online ISSN 1751-9683

Received 28/08/2013, Accepted 28/11/2013, Revised 15/11/2013, Published 23/04/2014

An analysis of robust estimation theory in the light of sparse signals reconstruction is considered. This approach is motivated by compressive sensing (CS) concept which aims to recover a complete signal from its randomly chosen, small set of samples. In order to recover missing samples, the authors define a new reconstruction algorithm. It is based on the property that the sum of generalised deviations of estimation errors, obtained from robust transform formulations, has different behaviour at signal and non-signal frequencies. Additionally, this algorithm establishes a connection between the robust estimation theory and CS. The effectiveness of the proposed approach is demonstrated on examples.

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Relationship between the robust statistics theory and sparse compressive sensed signals reconstruction

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