The curvelet transform for fusion of very-high resolution multispectral and panchromatic images

This paper presents a novel image fusion method, suitable for pan-sharpening of multispectral (MS) bands, based on multi-resolution analysis (MRA). The low-resolution MS bands are sharpened by injecting high-pass directional details extracted from the high-resolution panchromatic (Pan) image by means of the curvelet transform, which is a non-separable MRA, whose basis function are directional edges with progressively increasing resolution. The advantage with respect to conventional separable MRA, either decimated or not, is twofold: directional detail coefficients matching image edges may be preliminarily soft-thresholded to achieve denoising better than in the separable wavelet domain; modeling of the relationships between high-resolution detail coefficients of S bands and of the Pan image is more fitting, being carried out in a directional wavelet domain. Experiments carried out on a very-high resolution MS + Pan QuickBird image show that the proposed curvelet method quantitatively outperforms state-of-the art image fusion methods, in terms of geometric, radiometric, and spectral fidelity.