Fast Three-Dimensional Empirical Mode Decomposition of Hyperspectral Images for Class-Oriented Multitask Learning

In this paper, we propose a fast 3-D empirical mode decomposition (fTEMD) method for hyperspectral images (HSIs) to achieve class-oriented multitask learning (cMTL). The major steps of the proposed method are twofold: 1) fTEMD and 2) cMTL. On the one hand, the traditional empirical mode decomposition is extended to its 3-D version, which naturally treats the HSI as a cube and effectively decomposes the HSI into several 3-D intrinsic mode functions (TIMFs). To accelerate the fTEMD, 3-D Delaunay triangulation is adopted to determine the distances of extrema, whereas separable filters are implemented to generate the envelopes. On the other hand, cMTL is performed on the TIMFs by taking those TIMFs as features of different tasks. The proposed cMTL learns the representation coefficients by taking advantage of the class labels and fully exploiting the information contained in each TIMF. Experiments conducted on three benchmark data sets demonstrate the effectiveness of the proposed method.