Abstract
In microscopic image processing for analyzing biological objects, structural characters of objects such as symmetry and orientation can be used as a prior knowledge to improve the results. In this study, we incorporated filamentous local structures of neurons into a statistical model of image patches and then devised an image processing method based on tensor factorization with image patch rotation. Tensor factorization enabled us to incorporate correlation structure between neighboring pixels, and patch rotation helped us obtain image bases that well reproduce filamentous structures of neurons. We applied the proposed model to a microscopic image and found significant improvement in image restoration performance over existing methods, even with smaller number of bases.
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References
Muresan DD, Parks TW (2003) Adaptive principal components and image denoising. Int Conf Image Process 1:101–4
Olshausen BA, Field DJ (1996) Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381(6583):607–609
Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–45
Zhang L, Dong W, Zhang D, Shi G (2010) Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recognit 43:1531–1549
Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401(6755):788–91
Kim YD, Choi S (2007) Nonnegative tucker decomposition. In: IEEE Conference on computer vision and pattern recognition, pp 1–8
Carroll JD, Chang JJ (1970) Analysis of individual differences in multidimensional scaling via an n-way generalization of ‘Eckart–Young’ decomposition. Psychometrika 35(3):283–319
Harshman RA (1970) Foundations of the PARAFAC procedure: models and conditions for an ‘explanatory’ multimodal factor analysis. Comput Vis 16(1):1–84
Tucker LR (1966) Some mathematical notes on three-mode factor analysis. Psychometrika 31(3):279–311
Kroonenberg PM, Leeuw J (1980) Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika 45(1):69–97
De Lathauwer L, De Moor B, Vandewalle J (2000) A multilinear singular value decomposition. SIAM J Matrix Anal Appl 21(4):1253
De Lathauwer L, De Moor B, Vandewalle J (2000) On the best rank-1 and rank-(\(R_1,R_2,\ldots,R_N\)) approximation of higher-order tensors. SIAM J Matrix Anal Appl 21(4):1324–42
Sheehan BN, Saad Y (2007) Higher order orthogonal iteration of tensors (HOOI) and its relation to PCA and GLRAM. In: SIAM international conference on data mining. SIAM
Bader BW, Kolda TG (2012) MATLAB Tensor Toolbox Version 2.5. Available online
Blanter YM, Buttiker M (2000) Shot noise in mesoscopic conductors. Phys Rep 336:1–166
Acknowledgments
This study was supported by Grant-in-Aid for Scientific Research on Innovative Areas: ‘Mesoscopic neurocircuity: towards understanding of the functional and structural basis of brain information processing’ from MEXT, Japan.
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Kouno, M., Nakae, K., Oba, S. et al. Microscopic image restoration based on tensor factorization of rotated patches. Artif Life Robotics 17, 417–425 (2013). https://doi.org/10.1007/s10015-012-0077-6
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DOI: https://doi.org/10.1007/s10015-012-0077-6