A Variational Approach for Sharpening High Dimensional Images

Abstract

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,

The Optimized Block-Regression-Based Fusion Algorithm for Pansharpening of Very High Resolution Satellite Imagery

“…The fusion quality is assessed in two aspects, i.e., preservation of spectral characteristics and enhancement of spatial details (Möller et al, 2012;Saeedi and Faez, 2011;Witharana et al, 2013;Zhou et al, 2014). The used metrics for preservation of spectral characteristics are correlation coefficients (CC), root mean squared error (RMSE) (Möller et al, 2012;Saeedi and Faez, 2011;Witharana et al, 2013) and spectral angle mapper (SAM) (Alparone et al, 2007;Möller et al, 2012;Witharana et al, 2013;Zhou et al, 2014) between multispectral and fused images.…”

“…The used metrics for preservation of spectral characteristics are correlation coefficients (CC), root mean squared error (RMSE) (Möller et al, 2012;Saeedi and Faez, 2011;Witharana et al, 2013) and spectral angle mapper (SAM) (Alparone et al, 2007;Möller et al, 2012;Witharana et al, 2013;Zhou et al, 2014) between multispectral and fused images. The formula for calculating RMSE is as follows:…”

“…In order to address the problem, some researchers presented pan-sharpening methods with the capacity of adjustment (Chen et al, 2013;Choi, 2006;Fasbender et al, 2008;Möller et al, 2012;Te-Ming et al, 2012;Yee et al, 2014). Fusion results can be adapted by adjusting specific parameters to realize the different emphases between preservation of color characteristics and enhancement of spatial details.…”

“…Fusion results can be adapted by adjusting specific parameters to realize the different emphases between preservation of color characteristics and enhancement of spatial details. In order to achieve the adjustment, some of the existing algorithms need amendment of multiple parameters (Fasbender et al, 2008;Möller et al, 2012;Te-Ming et al, 2012). It is difficult to apply these algorithms in actual engineering projects.…”

A Parallel Computing Paradigm for Pan-Sharpening Algorithms of Remotely Sensed Images on a Multi-Core Computer

“…For the PCA method in the framework, the average correlation coefficient is lower than those from ERDAS and ENVI. Universal image quality index (UIQI) [85] widely used in the studies [31,35,86,87] is also calculated to evaluate the difference of sharpened images between algorithms in the framework and corresponding versions in commercial software. Table 9 indicates that the results of IHS and CN in the framework is better than in commercial software, while the UIQI value of PCA in the framework is lower than in commercial software.…”