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Ramanujan Sums (RS) have been found to be very successful in signal processing recently. However, as far as we know, the RS have not been applied to image analysis. In this paper, we propose two novel algorithms for image analysis, including moment invariants and pattern recognition. Our algorithms are invariant to the translation, rotation and scaling of the 2D shapes. The RS are robust to Gaussian white noise and occlusion as well. Our algorithms compare favourably to the dual-tree complex wavelet (DTCWT) moments and the Zernike's moments in terms of correct classification rates for three well-known shape datasets. [ABSTRACT FROM AUTHOR]

In this paper, a novel super-resolution method for hyperspectral imagery is proposed by using complex ridgelet transform. A Radon transform is first applied to each band image of a datacube to be enhanced to obtain the Radon slices, and then a 1D dual-tree complex wavelet transform is conducted along each Radon slice to generate coefficients of the complex ridgelet transform. The ordinary ridgelet transform or the finite ridgelet transform (FRIT), however, uses the 1D scalar wavelet transform instead of the dual-tree complex wavelet transform along each Radon slice. The reason why the dual-tree complex wavelet is adopted in this paper is because it has the property of approximate shift invariance, which is very important in image super-resolution. Experiments are conducted in this paper to demonstrate the advantages of the proposed method over the wavelet super-resolution, the FRIT image fusion, and the principal component analysis fusion. [ABSTRACT FROM AUTHOR]

Since Donoho et al. proposed the wavelet thresholding method for signal denoising, many different denoising approaches have been suggested. In this paper, we present three different wavelet shrinkage methods, namely NeighShrink, NeighSure and NeighLevel. NeighShrink thresholds the wavelet coefficients based on Donoho's universal threshold and the sum of the squares of all the wavelet coefficients within a neighborhood window. NeighSure adopts Stein's unbiased risk estimator (SURE) instead of the universal threshold of NeighShrink so as to obtain the optimal threshold with minimum risk for each subband. NeighLevel uses parent coefficients in a coarser level as well as neighbors in the same subband. We also apply a multiplying factor for the optimal universal threshold in order to get better denoising results. We found that the value of the constant is about the same for different kinds and sizes of images. Experimental results show that our methods give comparatively higher peak signal to noise ratio (PSNR), are much more efficient and have less visual artifacts compared to other methods. [ABSTRACT FROM AUTHOR]