Abstract-The goal of pan-sharpening is to fuse a low spatial resolution multispectral image with a higher resolution panchromatic image to obtain an image with high spectral and spatial resolution. The Intensity-Hue-Saturation (IHS) method is a popular pan-sharpening method used for its efficiency and high spatial resolution. However, the final image produced experiences spectral distortion. In this letter, we introduce two new modifications to improve the spectral quality of the image. First, we propose imageadaptive coefficients for IHS to obtain more accurate spectral resolution. Second, an edge-adaptive IHS method was proposed to enforce spectral fidelity away from the edges. Experimental results show that these two modifications improve spectral resolution compared to the original IHS and we propose an adaptive IHS that incorporates these two techniques. The adaptive IHS method produces images with higher spectral resolution while maintaining the high-quality spatial resolution of the original IHS.

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Abstract. Earth observing satellites usually not only take ordinary red-green-blue images, but provide several images including the near-infrared and infrared spectrum. These images are called multispectral, for about four to seven different bands, or hyperspectral, for higher dimensional images of up to 210 bands. The drawback of the additional spectral information is that each spectral band has rather low spatial resolution. In this paper we propose a new variational method for sharpening high dimensional spectral images with the help of a high resolution gray scale image while preserving the spectral characteristics used for classification and identification tasks. We describe the application of Split Bregman minimization to our energy, prove convergence speed and compare the Split Bregman method to a descent method based on the ideas of alternating directions minimization. Finally, we show results on Quickbird multispectral as well as on AVIRIS hyperspectral data.Key words. image fusion, multispectral, hyperspectral, pan-sharpening, variational 1. Introduction. Instead of just taking red-green-blue images many satellite imaging systems, such as the Quickbird and Landsat-7 satellites, produce so-called multispectral images including the near-infrared spectrum and consist of four to seven bands. These additional bands can be used for various identification and classification tasks. Because images in a precise spectral range can only be taken at rather low spectral resolution, many satellites also include a so-called panchromatic image, which is a gray-scale image that spans a wide range of frequencies, but comes at high spatial resolution. Pan-sharpening is the process of fusing the low resolution multispectral image with the high resolution panchromatic image to obtain a high resolution multispectral image.The goal of pan-sharpening is to combine the high spatial resolution of the panchromatic image with the precise spectral information of the multispectral image. The resulting image should have high visual quality to aid in detection and classification tasks. However, the pan-sharpened image should also contain the same spectral (color) information as the original multispectral data for precise identification of targets.Several methods have been proposed for pan-sharpening multispectral imagery. Many techniques express the panchromatic image as a linear combination of the multispectral bands, including the Intensity-Hue-Saturation (IHS) ([17, 16, 44]) and Brovey methods ([22]). Other methods project the images into a different space like Principal Component Analysis (PCA) ([42]). Several authors have proposed using the wavelet transform or other types of MRA to extract geometric edge information from the panchromatic image. These details are injected into the low resolution image,

There has been significant research on pan-sharpening multispectral imagery with a high resolution image, but there has been little work extending the procedure to high dimensional hyperspectral imagery. We present a wavelet-based variational method for fusing a high resolution image and a hyperspectral image with an arbitrary number of bands. To ensure that the fused image can be used for tasks such as classification and detection, we explicitly enforce spectral coherence in the fusion process. This procedure produces images with both high spatial and spectral quality. We demonstrate this procedure on several AVIRIS and HYDICE images.

Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these methods could result in nonnegligible portions of the support of the density in unrealistic geographic locations. For example, crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans, mountains, and so forth. We propose a set of Maximum Penalized Likelihood Estimation methods based on Total Variation and H 1 Sobolev norm regularizers in conjunction with a priori high resolution spatial data to obtain more geographically accurate density estimates. We apply this method to a residential burglary data set of the San Fernando Valley using geographic features obtained from satellite images of the region and housing density information.