Advantages of Laplacian pyramids over “` a trous” wavelet transforms for pansharpening of multispectral images Bruno Aiazzi a , Luciano Alparone a,b , Stefano Baronti a , Andrea Garzelli a,c , Massimo Selva a a “Nello Carrara” Institute of Applied Physics, Research Area of Florence, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy b Department of Electronics & Telecommunications, University of Florence, Via Santa Marta 3, 50139 Florence, Italy c Department of Information Engineering, University of Siena, Via Roma 56, 53100 Siena, Italy Keywords: Aliasing, “` a trous” wavelet, data fusion, Laplacian pyramid, multiresolution analysis, pansharpening. ABSTRACT The advantages provided by the generalized Laplacian pyramid (GLP) over the widespread “` a trous” wavelet (ATW) transform for multispectral (MS) pansharpening based on multiresolution analysis (MRA) are investigated. The most notable difference depends on the way GLP and ATW deal with aliasing possibly occurring in the MS data, which is originated by insufficient sampling step size, or equivalently by a too high amplitude value of the modulation transfer function (MTF) at Nyquist frequency and may generate annoying jagged patterns that survive in the sharpened image. In this paper, it is proven that GLP is capable of compensating the aliasing of MS, unlike ATW, and analogously to component substitution (CS) fusion methods, thanks to the decimation and interpolation stages present in its flowchart. Experimental results will be presented in terms of quality/distortion global score indexes (SAM, ERGAS and Q4) for increasing amounts of aliasing, measured by the amplitude at Nyquist frequency of the Gaussian-like lowpass filter simulating the average MTF of the individual spectral channels of the instrument. GLP and ATW-based methods, both using the same MTF filters and the same global injection gain, will be compared to show the advantages of GLP over ATW in the presence of aliasing of the MS bands. 1. INTRODUCTION Pansharpening is a branch of data fusion that is receiving an ever increasing attention from the remote sensing community. New-generation spaceborne imaging sensors operating in a variety of ground scales and spectral bands provide huge volumes of data having complementary spatial and spectral resolutions. Constraints on the signal to noise ratio (SNR) impose that the spatial resolution must be lower, if the requested spectral resolution is higher. Conversely, the highest spatial resolution is obtained by a (Pan) panchromatic image, in which spectral diversity is missing. The tradeoff of spectral and spatial resolution makes it desirable to perform a spatial resolution enhancement of the lower resolution multispectral (MS) data or, equivalently, to increase the spectral resolution of the data set having a higher ground resolution, but a lower spectral resolution; as a limit case, constituted by a unique Pan image bearing no spectral information. According to the most recent studies carried out by the authors, 1 the majority of image fusion methods can be divided into two main classes. Such classes uniquely differ in the way the spatial details are extracted from the Pan image. • Techniques that employ linear space-invariant digital filtering of the Pan image to extract the spatial details that will be added to the MS bands; all methods employing multiresolution analysis (MRA) belong to this class. • Techniques that yield the spatial details as pixel difference between the Pan image and a nonzero-mean component obtained from a spectral transformation of the MS bands, without any spatial filtering of the former. They are equivalent to substitution of such a component with the Pan image followed by reverse transformation to produce the sharpened MS bands. 2 Further author information: (Send correspondence to A. Garzelli) B.A.: E-mail: b.aiazzi@ifac.cnr.it, Telephone: +39 055 5226451 L.A.: E-mail: alparone@lci.det.unifi.it, Telephone: +39 055 4796563 S.B.: E-mail: s.baronti@ifac.cnr.it, Telephone: +39 055 5226450 A.G.: E-mail: garzelli@dii.unisi.it, Telephone: +39 0577 1606129 M.S.: E-mail: m.selva@ifac.cnr.it, Telephone: +39 055 5226417. Image and Signal Processing for Remote Sensing XVIII, edited by Lorenzo Bruzzone, Proc. of SPIE Vol. 8537, 853704 · © 2012 SPIE · CCC code: 0277-786/12/$18 doi: 10.1117/12.976298 Proc. of SPIE Vol. 8537 853704-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/28/2012 Terms of Use: http://spiedl.org/terms