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Automatic Target Detection for Sparse Hyperspectral Images

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Hyperspectral Image Analysis

Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

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Abstract

In this work, a novel target detector for hyperspectral imagery is developed. The detector is independent on the unknown covariance matrix, behaves well in large dimensions, distributional free, invariant to atmospheric effects, and does not require a background dictionary to be constructed. Based on a modification of the robust principal component analysis (RPCA), a given hyperspectral image (HSI) is regarded as being made up of the sum of a low-rank background HSI and a sparse target HSI that contains the targets based on a pre-learned target dictionary specified by the user. The sparse component is directly used for the detection, that is, the targets are simply detected at the non-zero entries of the sparse target HSI. Hence, a novel target detector is developed, which is simply a sparse HSI generated automatically from the original HSI, but containing only the targets with the background is suppressed. The detector is evaluated on real experiments, and the results of which demonstrate its effectiveness for hyperspectral target detection especially when the targets are well matched to the surroundings.

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Notes

  1. 1.

    A natural suggestion could be that the rank of \(\mathbf {L}\) usually has a physical meaning (e.g., number of endmembers in background), and thus, why not to minimize the latter two terms in Eq. (15.2) with the constraint that the rank of \(\mathbf {L}\) should not be larger than a fixed value d? That is,

    $$ \underset{\mathbf {L}, \mathbf {C}}{\mathrm {min}} \, \left\{ \lambda \,\left\| \mathbf {C}\right\| _{2,1} + \left\| \mathbf {D} - \mathbf {L} - \left( \mathbf {A}_t \mathbf {C}\right) ^T\right\| _F^2 \right\} \,, ~~s.t.~~ \mathrm {rank}(\mathbf {L}) \le d. $$

    In our opinion, assuming that the number of endmembers in background is known exactly will be a strong assumption and our work will be less general as a result. One can assume d to be some upper bound, in which case, the suggested formulation is a possible one. However, solving such a problem (with a hard constraint that the rank should not exceed some bound) is in general a NP-hard problem, unless there happens to be some special form in the objective which allows for a tractable solution. Thus, we adopt the soft constraint form with the nuclear norm as a proxy for the rank of \(\mathbf {L}\); this is an approximation commonly done in the field and is found to give good solutions in many problems empirically.

  2. 2.

    We regret that in our work in [51, 52], we missed to add “221–224” with the other bands that are removed. Adding “221–224” will give exactly a total of 186 bands.

  3. 3.

    The MATLAB code of the proposed detector and experiments is available upon request. Please feel free to contact Ahmad W. Bitar.

  4. 4.

    We thank Dr. Gregg A. Swayze from the United States Geological Survey (USGS) who has suggested us to evaluate our model (15.2) on the distinction between alunite and kaolinite minerals.

  5. 5.

    We have been inspired by Fig. 8D-E in [75] to provide a close example of it in this chapter as can be shown in Fig. 15.4.

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Acknowledgements

The authors would greatly thank Dr. Gregg A. Swayze from the United States Geological Survey (USGS) for his time in providing them helpful remarks about the cuprite data and especially on the buddingtonite, alunite, and kaolinite minerals. They would also like to thank the handling editors (Prof. Saurabh Prasad and Prof. Jocelyn Chanussot) and some other anonymous reviewers for the careful reading and helpful remarks/suggestions.

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Authors and Affiliations

  1. SONDRA Lab/CentraleSupélec, Université Paris-Saclay, 91192, Gif-sur-Yvette, France

    Ahmad W. Bitar & Jean-Philippe Ovarlez

  2. Department of Electrical and Computer Engineering, American University of Beirut, Beirut, Lebanon

    Ahmad W. Bitar & Ali Chehab

  3. The French Aerospace Lab (ONERA), Université Paris-Saclay, 91120, Palaiseau, France

    Jean-Philippe Ovarlez

  4. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Loong-Fah Cheong

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  1. Ahmad W. Bitar
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Correspondence to Ahmad W. Bitar .

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  1. Department of Electrical and Computer Engineering, University of Houston, Houston, TX, USA

    Saurabh Prasad

  2. CNRS, Grenoble INP, GIPSA-lab, Université Grenoble Alpes, Grenoble, France

    Jocelyn Chanussot

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Bitar, A.W., Ovarlez, JP., Cheong, LF., Chehab, A. (2020). Automatic Target Detection for Sparse Hyperspectral Images. In: Prasad, S., Chanussot, J. (eds) Hyperspectral Image Analysis. Advances in Computer Vision and Pattern Recognition. Springer, Cham. https://doi.org/10.1007/978-3-030-38617-7_15

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