By Miloš Oravec
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Starck, J. ; Donoho, D. L. & Candes, E. J. (2002). Astronomical image representation by curvelet transform, Astronomy & Astrophysics, vol. 398, pp. 785–800, 2002. Starck, J. ; Candes, E. J. & Donoho, D. L. (2003). Gray and color image contrast enhancement by the curvelet transform, IEEE Transactions on Image Processing, vol. 12, pp. 706–717, 2003. Starck, J. ; Nguyen, M. K. & Murtagh, F. (2003). Deconvolution based on the curvelet transform, Proc. International Conference Image Processing, 2003.
The training set is the same as in the first experiment. 5. e. 5b). 5b), one can also note that 2D-PCA (or 2D-SVD) performs a little better than ND-PCA scheme when only a small number of principal components are used. In our opinion, there is no visible difference in the reconstruction quality between 2D-PCA (or 2D-SVD) and ND-PCA scheme with a small number of An Extension of Principal Component Analysis 31 singular values. e. all voxel values are set to zero except the voxels on the face surface), it is therefore more sensitive to computational errors compared to a 2D still image.
4. Find the error between the reconstructed sample and the given test sample by error (vtest , i ) || vk ,test vrecon (i ) ||2 . 5. Once the error for every class is obtained, choose the class having the minimum error as the class of the given test sample. The main workhorse behind the SC algorithm is the optimization problem (5). The rest of the steps are straightforward. We give a very simple algorithm to solve this optimization problem. IRLS algorithm for l1 minimization xˆ (0) min || y Ax ||2 2 by conjugate Initialization – set δ(0) = 0 and find the initial gradient method.