We develop a method for superresolution based on anisotropic harmonic analysis. Our ambition is to efficiently increase the resolution of an image without blurring or introducing artifacts, and without integrating additional information, such as sub-pixel shifts of the same image at lower resolutions or multimodal images of the same scene. The approach developed in this article is based on analysis of the directional features present in the image that is to be superesolved. The harmonic analytic technique of shearlets is implemented in order to efficiently capture the directional information present in the image, which is then used to provide smooth, accurate images at higher resolutions. Our algorithm is compared to both a recent anisotropic technique based on frame theory and circulant matrices,1 as well as to the standard superresolution method of bicubic interpolation. We evaluate our algorithm on synthetic test images, as well as a hyperspectral image. Our results indicate the superior performance of anisotropic methods, when compared to standard bicubic interpolation.
We propose a framework for analyzing and visualizing data at multiple scales and directions by constructing a novel class of tight frames. We describe an elegant way of creating 2D tight frames from 1D sets of orthonormal vectors and show how to exploit the representation redundancy in a computationally efficient manner. Finally, we employ this framework to perform image superresolution via edge detection and characterization.
Several studies have reported that the use of derived spectral features, in addition to the original hyperspectral data, can
facilitate the separation of similar classes. Linear and nonlinear transformations are employed to project data into
mathematical spaces with the expectation that the decision surfaces separating similar classes become well defined.
Therefore, the problem of discerning similar classes in expanded space becomes more tractable. Recent work presented
by one of the authors discusses a dimension expansion technique based on generating real and imaginary complex
features from the original hyperspectral signatures. A complex spectral angle mapper was employed to classify the data.
In this paper, we extend this method to include other approaches that generate derivative-like and wavelet-based spectral
features from the original data. These methods were tested with several supervised classification methods with two
Hyperspectral Image (HSI) cubes.
Advances in hyperspectral sensor technology increasingly provide higher resolution and higher quality data for the accurate generation of terrain categorization/classification (TERCAT) maps. The generation of TERCAT maps from hyperspectral imagery can be accomplished using a variety of spectral pattern analysis algorithms; however, the algorithms are sometimes complex, and the training of such algorithms can be tedious. Further, hyperspectral imagery contains a voluminous amount of data with contiguous spectral bands being highly correlated. These highly correlated bands tend to provide redundant information for classification/feature extraction computations. In this paper, we introduce the use of wavelets to generate a set of Generalized Difference Feature Index (GDFI) measures, which transforms a hyperspectral image cube into a derived set of GDFI bands. A commonly known special case of the proposed GDFI approach is the Normalized Difference Vegetation Index (NDVI) measure, which seeks to emphasize vegetation in a scene. Numerous other band-ratio measures that emphasize other specific ground features can be shown to be a special case of the proposed GDFI approach. Generating a set of GDFI bands is fast and simple. However, the number of possible bands is capacious and only a few of these “generalized ratios” will be useful. Judicious data mining of the large set of GDFI bands produces a small subset of GDFI bands designed to extract specific TERCAT features. We extract/classify several terrain features and we compare our results with the results of a more sophisticated neural network feature extraction routine.
The effect of using Adaptive Wavelets is investigated for dimension reduction and noise filtering of hyperspectral imagery that is to be subsequently exploited for classification or subpixel analysis. The method is investigated as a possible alternative to the Minimum Noise Fraction (MNF) transform as a preprocessing tool. Unlike the MNF method, the wavelet-transformed method does not require an estimate of the noise covariance matrix that can often be difficult to obtain for complex scenes (such as urban scenes). Another desirable characteristic of the proposed wavelet transformed data is that, unlike Principal Component Analysis (PCA) transformed data, it maintains the same spectral shapes as the original data (the spectra are simply smoothed). In the experiment, an adaptive wavelet image cube is generated using four orthogonal conditions and three vanishing moment conditions. The classification performance of a Derivative Distance Squared (DDS) classifier and a Multilayer Feedforward Network (MLFN) neural network classifier applied to the wavelet cubes is then observed. The performance of the Constrained Energy Minimization (CEM) matched-filter algorithm applied to this data us also observed. HYDICE 210-band imagery containing a moderate amount of noise is used for the analysis so that the noise-filtering properties of the transform can be emphasized. Trials are conducted on a challenging scene with significant locally varying statistics that contains a diverse range of terrain features. The proposed wavelet approach can be automated to require no input from the user.
For dimension reduction of hyperspectral imagery, we propose a modification to Principal Component Analysis (PCA), Karhunen-Loeve Transform, by choosing a set of basis vectors corresponding to the proposed transformation to be not only orthonormal but also wavelets. Although the eigenvectors of the covariance matrix of PCA minimize the mean square error over all other choices of orthonormal basis vectors, we will show that the proposed set of wavelet basis vectors have several desirable properties. After reducing the dimensionality of the data, we perform a supervised classification of the original and reduced data sets, compare the results, and assess the merits of such transformation.
We investigate a hyperspectral data reduction technique based on a matrix factorization method using the notion of linear independence instead of information measure, as an alternative to Principal Component Analysis (PCA) or the Karhunen-Loeve Transform. The technique is applied to a hyperspectral database whose spectral samples are known. We proceed to cluster such dimension-reduced databases with an unsupervised second order statistics clustering method and we compare those results to those produced by first order statistics. We illustrate the above methodology by applying it to several spectral databases. Since we know the class to which each sample belongs to in the database, we can effectively assess the algorithms' clustering/classification accuracy. In addition to using unsupervised clustering of data for purposes of image segmentation, we investigate this algorithm as a means for improving the integrity of spectral databases by removing spurious samples.
This paper discusses the nonuniform illumination of individual pixels in an array that is intrinsic to the scene viewed, as opposed to turbulence or platform motion as an error source in quantitative imagery. It describes two classes of algorithms to treat this type of problem. It points out that this problem can be viewed as a type of inverse problem with a corresponding integral equation unlike those commonly treated in the literature. One class allows estimation of the spatial variation of radiance within pixels using the single digital number irradiances produced by the measurements of the detectors within their instantaneous-fields-of-view (IFOVs). Usually it is assumed without discussion that the intrapixel radiance distribution is constant. Results are presented showing the improvements obtained by the methods discussed.
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