TOTAL VARIATION BASED HYPERSPECTRAL FEATURE EXTRACTION Behnood Rasti, Johannes R. Sveinsson and Magnus O. Ulfarsson University of Iceland Faculty of Electrical and Computer Engineering Hjardarhagi 2-6. IS-107 Reykjavik, Iceland ABSTRACT In this paper, a hyperspectral feature extraction method is proposed. A low-rank linear model using the right eigen- vector of the observed data is given for hyperspectral images. A total variation (TV) based regularization called Low-Rank TV regularization (LRTV) is used for hyperspectral feature extraction. The feature extraction is used for hyperspectral image classification. The classification accuracies obtained are significantly better than the ones obtained using features extracted by Principal Component Analysis (PCA) and Max- imum Noise Fraction (MNF). Index Terms— Feature extraction, hyperspectral image, low-rank model, regularization, total variation. 1. INTRODUCTION Hyperspectral images contain spatial and spectral information of a scene. A hyperspectral sensor has the ability to produce contiguous spectra. Thus, unlike the multispectral images, hyperspectral images contain detailed spectral information of a scene. Due to the uniqueness of the spectral signatures of materials, these type of images have been found very useful for recognizing the type of the materials in the captured scene. Total Variation (TV) was originally used for noise reduc- tion in [1]. A fast algorithm was given in [2] to solve the TV regularization efficiently. In addition to the broad research area in image processing, TV regularization has been widely used in remote sensing applications such as pansharpening [3], Synthetic Aperture Radar (SAR) denoising [4], hyper- spectral image denoising [5], hyperspectral image compres- sion [6] and hyperspectral unmixing [7, 8]. Hyperspectral images are usually very large, therefore their analysis is challenging. As a result, dimensionality re- duction has been a very active research area in hyperspectral image analysis. Terms such as feature extraction, feature reduction, feature selection and band selection etc. all refer to dimensionality reduction methods which simplify hyper- spectral image analysis. Due to spectral redundancy these This work was supported by the Doctoral Grants of the University of Iceland Research Fund and the University of Iceland Research Fund, and the Icelandic research fund (130635051). methods seek a low-rank representation of the hyperspectral data [9]. Principal Component Analysis (PCA) has been widely used in hyperspectral image analysis. The first few principal components usually capture the majority of the variance of the data set are usually used for processing. Since PCA is an orthogonal projection based on the largest signal variances, the principal components can have low Signal to Noise Ra- tios (SNR). Maximum Noise Fraction (MNF) [10] and Noise Adjusted Principal Components (NAPC) [11] have been de- veloped to increase the SNR of the extracted components. In this paper, a regularizing criterion is given for hyper- spectral Feature Extraction called Low-Ranked TV regular- ization (LRTVFE). A hyperspectral image is modeled based on a few features (components) and the low-rank matrix which contains the right eigenvectors of the observed im- age. The unknown reduced features are estimated by LRTV. The estimated features are classified using Support Vector Machine (SVM) and Random Forest (RF) classifiers. It is shown that the classification accuracies obtained by LRTVFE are significantly better than the ones obtained using features extracted by PCA and MNF [10]. The rest of the paper is organized as follows. A low-rank model is given in Section 2 for hyperspectral images. Hy- perspectral feature extraction using LRTV regularization is discussed in Section 3. The experimental results are given in Section 4. Finally, Section 5 concludes the paper. 2. HYPERSPECTRAL MODEL A hyperspectral image can be modeled by Y = X + N, where Y =  y (i)  is an n×p matrix containing the vectorized observed image at band i in its ith columns, X =  x (i)  is an n × p matrix containing the vectorized unknown image at band i in its ith columns and N =  n (i)  is an n × p matrix containing the vectorized zero-mean Gaussian noise at band i in its ith columns. After whitening the noise between bands we get the model ˜ Y = ˜ X + ˜ N, 4644 978-1-4799-5775-0/14/$31.00 ©2014 IEEE IGARSS 2014