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Chebyshev-Fourier moments for describing images were proposed. After definition of the moments, the multidistortion invariance of the moments was verified. The performance of the moments in describing images was investigated in terms of the normalized image-reconstruction error and the results of the experiments on the noise sensitivity are given.

We propose radial harmonic Fourier moments, which are shifting, scaling, rotation, and intensity invariant. Compared with Chebyshev-Fourier moments, the new moments have superior performance near the origin and better ability to describe small images in terms of image-reconstruction errors and noise sensitivity. A multidistortion-invariant pattern-recognition experiment was performed with radial harmonic Fourier moments.

Pseudo-Jacobi (p = 4, q = 3)-Fourier moments (PJFMs) based on Jacobi polynomials are described. The new orthogonal radial polynomials have almost uniformly distributed (n + 2) zeros in the region of small radial distance 0 < or = r < or = 1. Both theoretical and experimental results indicate that PJFMs are better than orthogonal Fourier-Mellin moments in terms of reconstruction errors and signal-to-noise ratio. The PJFMs are normalized to shift, rotation, scale, and intensity invariance, and some pattern-recognition experiments are described.

As an effective approach to gain the high-spatial-resolution hyperspectral images, data fusion is usually adopted to enhance the spatial resolution of hyperspectral images by the spatial information of multispectral images. In this paper, in order to remove the ill-posedness of well-known coupled non-negative matrix factorization, we formulate a well-posed fusion problem by incorporating total variation and signature-based regularizations for image smoothing and high-fidelity signature reconstruction. Then, the problem can be decoupled into two convex subproblems, which yield closed-form solutions separately by the alternating direction method of multipliers algorithms. Due to the large sizes of the problems, a few of constructed matrices and tensor operations are employed to simplify the expressions for reducing the computational complexities. Simulation and experimental results not only demonstrate that the performance of the proposed fusion algorithm is much better than that of state-of-the-art methods but also show that the total variation and signature-based regularizers are of paramount importance in yielding the high-spatialresolution hyperspectral images. INDEX TERMS Total variation, CNMF, data fusion, alternating direction method of multipliers.