Sparse Subspace Clustering in Hyperspectral Images using Incomplete Pixels
Spectral image clustering is an unsupervised classification method which identifies distributions of pixels using spectral information without requiring a previous training stage. The sparse subspace clustering-based methods (SSC) assume that hyperspectral images lie in the union of multiple low-dimensional subspaces. Using this, SSC groups spectral signatures in different subspaces, expressing each spectral signature as a sparse linear combination of all pixels, ensuring that the non-zero elements belong to the same class. Although these methods have shown good accuracy for unsupervised classification of hyperspectral images, the computational complexity becomes intractable as the number of pixels increases, i.e. when the spatial dimension of the image is large. For this reason, this paper proposes to reduce the number of pixels to be classified in the hyperspectral image, and later, the clustering results for the missing pixels are obtained by exploiting the spatial information. Specifically, this work proposes two methodologies to remove the pixels, the first one is based on spatial blue noise distribution which reduces the probability to remove cluster of neighboring pixels, and the second is a sub-sampling procedure that eliminates every two contiguous pixels, preserving the spatial structure of the scene. The performance of the proposed spectral image clustering framework is evaluated in three datasets showing that a similar accuracy is obtained when up to 50% of the pixels are removed, in addition, it is up to 7.9 times faster compared to the classification of the data sets without incomplete pixels.
M. Fauvel, J. Chanussot, J. A. Benediktsson, and J. R. Sveinsson, “Spectral and spatial classification of hyperspectral data using SVMs and morphological profiles,” in 2007 IEEE International Geoscience and Remote Sensing Symposium,Barcelona 2007, vol. 46, no. 11, pp. 4834–4837. https://doi.org/10.1109/IGARSS.2007.4423943
N. M. Nasrabadi, “Hyperspectral Target Detection : An Overview of Current and Future Challenges,” IEEE Signal Process. Mag., vol. 31, no. 1, pp. 34–44, Jan. 2013. https://doi.org/10.1109/MSP.2013.2278992
J. M. Bioucas-Dias et al., “Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 5, no. 2, pp. 354–379, Apr. 2012. https://doi.org/10.1109/JSTARS.2012.2194696
G. Martin and J. M. Bioucas-Dias, “Hyperspectral Blind Reconstruction From Random Spectral Projections,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 9, no. 6, pp. 2390–2399, Jan. 2016. https://doi.org/10.1109/JSTARS.2016.2541541
A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging Spectrometry for Earth Remote Sensing,” Science (80-. )., vol. 228, no. 4704, pp. 1147–1153, Jun. 1985. https://doi.org/10.1126/science.228.4704.1147
Y. Liu, H. Pu, and D.-W. Sun, “Hyperspectral imaging technique for evaluating food quality and safety during various processes: A review of recent applications,” Trends Food Sci. Technol., vol. 69, pp. 25–35, Nov. 2017. https://doi.org/10.1016/j.tifs.2017.08.013
T. Adão et al., “Hyperspectral Imaging: A Review on UAV-Based Sensors, Data Processing and Applications for Agriculture and Forestry,” Remote Sens., vol. 9, no. 11, p. 1110, Oct. 2017. https://doi.org/10.3390/rs9111110
E. Elhamifar and R. Vidal, “Sparse Subspace Clustering: Algorithm, Theory, and Applications,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 11, pp. 2765–2781, Nov. 2013. https://doi.org/10.1109/TPAMI.2013.57
H. Zhang, H. Zhai, L. Zhang, and P. Li, “Spectral–Spatial Sparse Subspace Clustering for Hyperspectral Remote Sensing Images,” IEEE Trans. Geosci. Remote Sens., vol. 54, no. 6, pp. 3672–3684, Jun. 2016.
J. Bacca, C. V Correa, and H. Arguello, “Noniterative Hyperspectral Image Reconstruction From Compressive Fused Measurements,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 12, no. 4, pp. 1231–1239, Apr. 2019.
J. Dougherty, R. Kohavi, and M. Sahami, “Supervised and Unsupervised Discretization of Continuous Features,” in Machine Learning Proceedings,California.1995 . pp. 194–202.
Y. Liu, H. Pu, and D.-W. Sun, “Hyperspectral imaging technique for evaluating food quality and safety during various processes: A review of recent applications,” Trends Food Sci. Technol., vol. 69, no. 5, pp. 25–35, Nov. 2017. https://doi.org/10.1016/j.tifs.2017.08.013
S. Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inf. theory, vol. 28, no. 2, pp. 129–137, 1982.
G. H. Ball and D. J. Hall, “ISODATA, a novel method of data analysis and pattern classification,” 1965.
W. Pedrycz, “Fuzzy sets in pattern recognition: Methodology and methods,” Pattern Recognit., vol. 23, no. 1–2, pp. 121–146, Jan. 1990. https://doi.org/10.1016/0031-3203(90)90054-O
A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science. (80-. )., vol. 344, no. 6191, pp. 1492–1496, Jun. 2014. https://doi.org/10.1126/science.1242072
S. Vijendra, “Efficient Clustering for High Dimensional Data: Subspace Based Clustering and Density Based Clustering,” Inf. Technol. J., vol. 10, no. 6, pp. 1092–1105, Jun. 2011. https://doi.org/10.3923/itj.2011.1092.1105
Y. Zhong, L. Zhang, and W. Gong, “Unsupervised remote sensing image classification using an artificial immune network,” Int. J. Remote Sens., vol. 32, no. 19, pp. 5461–5483,Oct. 2011.
Y. Zhong, S. Zhang, and L. Zhang, “Automatic Fuzzy Clustering Based on Adaptive Multi-Objective Differential Evolution for Remote Sensing Imagery,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., vol. 6, no. 5, pp. 2290–2301, Oct 2013. https://doi.org/10.1109/JSTARS.2013.2240655
G. Chen and G. Lerman, “Spectral Curvature Clustering (SCC),” Int. J. Comput. Vis., vol. 81, no. 3, pp. 317–330, Mar. 2008. https://doi.org/10.1007/s11263-008-0178-9
C. A. Hinojosa, J. Bacca, and H. Arguello, “Spectral Imaging Subspace Clustering with 3-D Spatial Regularizer,” in Imaging and Applied Optics 2018 (3D, AO, AIO, COSI, DH, IS, LACSEA, LS&C, MATH, pcAOP), Orlando. 2018.
C. Hinojosa, J. Bacca, and H. Arguello, “Coded Aperture Design for Compressive Spectral Subspace Clustering,” IEEE J. Sel. Top. Signal Process., vol. 12, no. 6, pp. 1589–1600, Dec. 2018.
H. Zhang, H. Zhai, W. Liao, L. Cao, L. Zhang, and A. Pizurica, “Hyperspectral image kernel sparse subspace clustering with spatial max pooling operation,” 23rd Congr. Int., vol. 41, no. B3, pp. 945–948, 2016. https://pdfs.semanticscholar.org/ace6/0a31dbcd910ff7d722625aab5896b59022e0.pdf
E. Elhamifar and R. Vidal, “Sparse subspace clustering,” in 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami. 2009, pp. 2790–2797. https://doi.org/10.1109/CVPR.2009.5206547
C. V Correa, H. Arguello, and G. R. Arce, “Spatiotemporal blue noise coded aperture design for multi-shot compressive spectral imaging,” J. Opt. Soc. Am. A, vol. 33, no. 12, pp. 2312–2322, Dec. 2016.
H. Zhai, H. Zhang, L. Zhang, P. Li, and A. Plaza, “A New Sparse Subspace Clustering Algorithm for Hyperspectral Remote Sensing Imagery,” IEEE Geosci. Remote Sens. Lett., vol. 14, no. 1, pp. 43–47, Jan. 2017. https://doi.org/10.1109/LGRS.2016.2625200
S. Boyd, “Alternating direction method of multipliers,” in Talk at NIPS workshop on optimization and machine learning, California. 2011.
A. Y. Ng, M. I. Jordan, and Y. Weiss, “On spectral clustering: Analysis and an algorithm,” Adv. Neural Inf. Process. Syst., pp. 849–856, 2002.
J. Bacca, C. A. Hinojosa, and H. Arguello, “Kernel Sparse Subspace Clustering with Total Variation Denoising for Hyperspectral Remote Sensing Images,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP), Washington.2017. https://doi.org/10.1364/MATH.2017.MTu4C.5
Baumgardner, B. M. F., and L. L. L., “220 Band AVIRIS Hyperspectral Image Data Set: June 12, 1992 Indian Pine Test Site 3.” Purdue University. https://doi.org/10.4231/R7RX991C
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