A survey of classical methods and new trends in pansharpening of multispectral images <s> Methods based on the statistics of the image <s> A procedure is developed for combining high spatial resolution panchromatic data with lower resolution multispectral data in order to produce high spatial resolution digital data in multispectral form. Data simulating the French SPOT satellite were processed to resemble high altitude aerial photography, but image artifacts can hamper photointerpretative methods. <s> BIB001 </s> A survey of classical methods and new trends in pansharpening of multispectral images <s> Methods based on the statistics of the image <s> Abstract Multispectral image data fusion is understood here as a process that generates synthetic images from a combination of primary images, by attempting to preserve the best characteristics of each primary image. The obtained product is important in helping the users of remote sensing in visual analysis. This paper describes a new method for multispectral image data fusion using a Bayesian framework. As an example, the method is applied to the synthesis of new bands for the SPOT satellite. The method comprises two steps: (a) a new interpolator for the multispectral bands, obtained through the orthogonality principle and leading to the estimator and its covariance.matrix, which will be used as a priori information for the second step; and (b) a new statistical synthesis formulation, also obtained through the orthogonality principle, using as observations the panchromatic and the multispectral bands. Experimental results with SPOT images over Guarulhos Airport, Sao Paulo, Brazil, are presented, includin... <s> BIB002 </s> A survey of classical methods and new trends in pansharpening of multispectral images <s> Methods based on the statistics of the image <s> An improvement to an existing band correlation method is described for merging high spatial resolution imagery with data from additional lower spatial resolution bands. A figure of merit quantifies the improvement over pixel replication of the lower resolution imagery. Examples are given using AVIRIS data to simulate the future Landsat Thematic Mapper. A physical basis is useful in understanding results of the image sharpening procedure. <s> BIB003 </s> A survey of classical methods and new trends in pansharpening of multispectral images <s> Methods based on the statistics of the image <s> Due to the performance limit of remote sensing systems, multispectral images have limited spatial resolution. Their spatial resolution can be improved by merging them with higher resolution image data. A fundamental problem frequently occurring in existing fusion processes, however, is the distortion of spectral information. This paper presents a spatially adaptive image fusion algorithm which produces visually natural images and retains the quality of local spectral information as well. High frequency information of the high resolution image to be inserted to the resampled multispectral images is controlled by adaptive gains to incorporate the difference of local spectral characteristics between the high and the low resolution images into the fusion. Each gain is estimated to minimize the l 2-norm of the error between the original and the estimated pixel values defined in a spatially adaptive window of which the weights are proportional to the spectral correlation measurements of the corresponding region... <s> BIB004 </s> A survey of classical methods and new trends in pansharpening of multispectral images <s> Methods based on the statistics of the image <s> Currently, most optical Earth observation satellites carry both a panchromatic sensor and a set of lower spatialresolution multispectral sensors. In order to benefit from both sources of information, several pansharpening methods have been developed to produce a multispectral image at the spatial resolution of the panchromatic band. The aim of this paper is to suggest a novel approach to the pansharpening problem within a Bayesian framework. This Bayesian data fusion (BDF) method relies on statistical relationships between the various spectral bands and the panchromatic band without suffering from restricting modeling hypotheses. Furthermore, it allows the user to weight the spectral and panchromatic information with respect to either visual or quantitative criteria, which leads to adaptable results according to users' needs and study areas. The performance of this approach was compared to existing methods based on markedly different subset images from very high spatial resolution IKONOS images. Results showed that BDF yielded the highest spectral consistency. Furthermore, small details were adequately added to the pansharpened images with little artifact as compared to those created using wavelet-based methods. Finally, the method was fast and easy to implement owing to its straightforward formulation. As it does not have any intrinsic limitations on the type of data to be processed or the number of bands to be merged, it also appears to be very promising for optical/SAR or hyperspectral image fusion. <s> BIB005
The methods based on the statistics of the image include a set of methods that exploit the statistical characteristics of the MS and PAN images in the pansharpening process. The first known method in this family was proposed by Price BIB001 to combine PAN and MS imagery from dual-resolution satellite instruments based on the substantial redundancy existing in the PAN data and the local correlation between the PAN and MS images. Later, the method was improved by Price BIB003 by computing the local statistics of the images and by Park et al. BIB004 in the so-called spatially adaptive algorithm. Price's method BIB003 uses the statistical relationship between each band of the LRMS image and HR images to sharpen the former. It models the relationship between the pixels of each band of the HRMS z b , the PAN image x and the corresponding band of the LRMS image y b linearly as where y b is the band b of the LRMS image y upsampled to the size of the HRMS image by pixel replication,x represents the panchromatic image downsampled to the size of the MS image by averaging the pixels of x in the area covered by the pixels of y and upsampling again to its original size by pixel replication, andâ is a matrix defined as the upsampling, by pixel replication, of a weight matrix a whose elements are calculated from a window 3 × 3 of each LR image pixel. Price's algorithm succeeds in preserving the low-resolution radiometry in the fusion process, but sometimes, it produces blocking artifact because it uses the same weight for all the HR pixels corresponding to one LR pixel. If the HR and LR images have little correlation, the blocking artifacts will be severe. A pansharpened image using Price's method proposed in BIB003 is shown in Figure 3a . The spatially adaptive algorithm BIB004 starts from Price's method BIB003 , but with a more general and improved mathematical model. It features adaptive insertion of information according to the local correlation between the two images, preventing spectral distortion as much as possible and sharpening the MS images simultaneously. This algorithm has also the advantage that a number of high-resolution images, not only one PAN image, can be utilized as references of high-frequency information, which is not the case for most methods BIB004 . Besides those methods, most of the papers in this family have used the Bayesian framework to model the knowledge about the images and estimate the pansharpened image. Since the work of Mascarenhas BIB002 , a number of pansharpening methods have been proposed using the Bayesian framework (see  BIB005 