Nonnegative matrix factorizationbased hyperspectr

Authors: Zhou Zhang Zhenwei Shi

Publish Date: 2012/07/07

Volume: 23, Issue: 3-4, Pages: 895-905

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Abstract

The fusion of hyperspectral image and panchromatic image is an effective process to obtain an image with both high spatial and spectral resolutions However the spectral property stored in the original hyperspectral image is often distorted when using the class of traditional fusion techniques Therefore in this paper we show how explicitly incorporating the notion of “spectra preservation” to improve the spectral resolution of the fused image First a new fusion model spectral preservation based on nonnegative matrix factorization SPNMF is developed Additionally a multiplicative algorithm aiming at get the numerical solution of the proposed model is presented Finally experiments using synthetic and real data demonstrate the SPNMF is a superior fusion technique for it could improve the spatial resolutions of hyperspectral images with their spectral properties reliably preservedHyperspectral remote sensing is a new type of remote sensing that has attracted many people’s attention recently The hyperspectral image is a kind of threedimensional data two spatial dimensions and one spectral dimension 1 and thus is called “data cube” For each pixel the spectral dimension provides a continuous spectrum which has been widely used in a variety of applications such as target detection identification of natural and manmade materials 2 However due to the limitation of the imaging spectrometer the hyperspectral data has low spatial resolution which restricts the application of hyperspectral remote sensing in some fields Instead compared to the hyperspectral image the panchromatic image has high spatial resolution while no spectral information Therefore the fusion of hyperspectral and panchromatic image data has a possibility to produce the fused data with high spatial and spectral resolutionsThere are several studies on fusion algorithms and the most common ones can be separated into three categories 3 4 1 projection and substitution methods such as intensity hue and saturation transform IHS 5 2 different arithmetic combinations such as Brovey’s transform BT 6 3 the waveletbased fusion methods and those methods that inject spatial information from panchromatic images into hyperspectral or multispectral images such as discrete wavelet transform DWT 7 and highpass filtering HPF 8IHS transformation can effectively separate spatial intensity and spectral hue and saturation information from a standard RGB image To conduct an IHS image fusion intensity component I should be replaced by the panchromatic image If the intensity image of the IHS transform has a high correlation with the panchromatic image being used it will produce a satisfactory fusion result However in practice the intensity image and the panchromatic image often differ from each other to a certain extend Therefore a common problem of the IHS technique is the color distortion 9 10 BT is an IHSlike method 11 and it is based on the chromaticity transform 12 13 It is a simple fusion method while it would also cause spectral distortion Most literatures recognize that the main disadvantage of IHS and BT over other fusion techniques is that these two methods could only handle with threeband imagery 3 4 14 Hence they are not suitable to deal with the hyperspectral image which involves much more than three bandsRecently many researchers have focused on image fusion using wavelet transformation 15 16 The waveletbased fusion methods extract spatial detail information from a highresolution panchromatic image and then inject it into the hyperspectral bands In this manner owing to the detailed information extracted from the panchromatic image differs from the existing information in the original hyperspectral image the DWT method could also cause spectral distortion to some certain extend The HPF is similar to the DWT because they both inject the spatial features into the hyperspectral images during the fusion process However when we use the HPF method the spatial features are extracted using highpass filtering rather than the wavelet transform These two methods have a prominent advantage which is that they have the ability to handle images with arbitrary bands such as the hyperspectral imagesIn recent decades nonnegative matrix factorization NMF which was first proposed by DD Lee and HS Seung in 1999 17 has been successfully used in the field of hyperspectral image analysis and processing such as in the spectral unmixing 18 To unmix hyperspectral data the original image cube can be decomposed into the spectral matrix and the abundance matrix by using the NMF technique The hyperspectral images themselves often include largescale data generally stored in the form of matrices and the identification and the analysis of them are also implemented in the form of matrices In addition it is obvious that the gray of pixels is always nonnegative These characteristics make NMF indubitably become one popular technique for the hyperspectral image processingIn this paper we propose a new model called the spectral preservation based on nonnegative matrix factorization SPNMF for hyperspectral and panchromatic data fusion In the fusion we extract the feature of the hyperspectral data by NMF and enhance the feature with high spatial resolution image panchromatic image Besides in this new model a regularized term aiming at preserving the spectral information of the fused hyperspectral data is added based on the original NMF By combining these two parts fused hyperspectral data with both high spatial and spectral resolutions can be generated In addition both spatial and spectral reconstruction qualities are evaluated by three experiments using synthetic data and real data The results of comparison with other two traditional methods—HPF and DWT—are also providedThis paper is organized as follows Section 2 describes the SPNMF model for the hyperspectral and panchromatic data fusion Section 3 proposes the corresponding multiplicative algorithm which is used to get the numerical solution of the proposed model In Sect 4 experimental results both on synthetic and real data with different hyperspectral image fusion methods are discussed and finally close with conclusions in Sect 5

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