PCA transform multidimensional image data into a new, uncorrelated co-ordinate system or vector space. It produces a space in which the data have maximum variance along its first axis, the next largest variance along a second mutually orthogonal axis and so on. Sometimes even the lower-order PC's may contain valuable information. The later principal components would be expected, in general, to show little variance. These could be considered therefore to contribute little to separability and could be ignored, thereby reducing the essential dimensionality of the classification space and thus improving classification speed. Stated differently, the purpose of this process is to compress all the information contained in an original n – band data set into fewer than n “new bands” or component. The components are then used in lieu of the original data. These transformations may be applied as a preprocessing procedure prior to automated classification process of the data.
Minimum Noise Fraction (MNF)
The bands in a hyperspectral dataset have differing noise levels (S/N). It may be desirable to filter or remove those bands that contribute most to noise. When the bands of a hyperspectral dataset have differing amounts of noise, a standard principal components (PC) transform will not produce components with a steadily increasing noise level. This makes it difficult to select a cutoff point. To achieve a components dataset that does have increasing noise (decreasing S/N), a modified PC transform, termed the Minimum Noise Fraction (MNF) has been developed (Green et al. 1988, Lee et al. 1990). This transformation is mainly used to reduce the dimensionality of hyperspectral data and developed as an alternative to PCA. It is defined as a two-step cascaded PCA. The first step, based on an estimated noise covariance matrix, is to decorrelate and rescale the data noise, where the noise has unit variance and no band-to-band correlations. The next step is a standard PCA of the noise-whitened data. The MNF transformation is a linear transformation related to PC that orders the data according to signal-to-noise-ratio. It determines the inherent dimensionality of the data, segregates noise in the data and reduces the computational requirements for subsequent processing. It partitions the data space into two parts: one associated with large eigenvalues and coherent eigenimages, and a second with near-unity eigenvalues and noise-dominated images. By using only the coherent portions in subsequent processing, the noise is separated from the data, thus improving spectral processing results.
Ground/Laboratory Spectra Acquisition
Ground based/laboratory spectra acquisition is required to serve various purposes in the context of hyperspectral data acquisition and analysis. The purpose of collection of Ground based/laboratory spectra are for
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li>providing critical information for calibration of data and atmospheric correction,
Calibration and Atmospheric Correction
For obtaining accurate results calibrating and atmospheric correction is a requirement for most hyperspectral data analysis process. The identification and mapping of materials and material properties is best accomplished by deriving the fundamental properties of the surface, its reflectance, while removing the interfering effects of atmospheric absorption and scattering, the solar spectrum, and instrumental biases. Calibration to surface reflectance is inherently simple in concept, yet it is very complex in practice because atmospheric radiative transfer models and the solar spectrum have not been characterized with sufficient accuracy to correct the data to the precision of some currently available instruments, such as the NASA/JPL Airborne Visible and Infra-Red Imaging Spectrometer.
The objectives of calibrating remote sensing data are to remove the effects of the atmosphere (scattering and absorption) and to convert from radiance values received at the sensor to reflectance values of the land surface. The advantages offered by calibrated surface reflectance spectra compared to uncorrected radiance data include: 1) the shapes of the calibrated spectra are principally influenced by the chemical and physical properties of surface materials, 2) the calibrated remotely-sensed spectra can be compared with field and laboratory spectra of known materials, and 3) the calibrated data may be analyzed using spectroscopic methods that isolate absorption features and relate them to chemical bonds and physical properties of materials. Thus, greater confidence may be placed in the maps of derived from calibrated reflectance data, in which errors may be viewed to arise from problems in interpretation rather than incorrect input data.
Spectral Libraries
Spectral Libraries are collections of spectra of different surface materials generated from laboratory & ground based measurement and used as the reference against which hyperspectral imaging data are compared to determine earth surface material’s composition. Spectral libraries contain spectra of individual species, Often grouped by surface type (vegetation vs. soils vs. man-made materials etc.) and sometimes by grain size fraction (influence on spectra) acquired at test sites representative of varied terrain and climatic zones.These are principally used for identification of mineralogy, but also contain some spectra of vegetation, man-made materials, snow-ice, and water. There are a variety of spectral libraries for earth-surface materials available e.g. spectral library included in ENVI software and ASTER speclib on the internet.
Endmember extraction
Theoretically the existing pure features in mixed pixels are refered to as endmembers. Selection and identification of spectral endmembers in an image is the key point to success of the linear spectral mixing model. A set of endmembers should allow the description of all spectral variability for all pixels. Two different approaches have generally been used to define endmembers in a mixing model:
•Use of the existing library of reflectance spectra
•extraction of the purest pixels from the image data itself
Endmembers resulting through the first option are denoted as known endmembers whereas the second option results in derived endmembers. Because of the difficulties of access to spectral library or field measurement of spectral properties of land cover types of interest, endmember data of the known ground cover types can be extracted from the Hyperspectral data.
The Pixel Purity Index (PPI)
algorithm for Endmember selection is based on the geometry of convex sets. A dimensionality reduction is first performed using the MNF transform. Next, a pixel purity index is calculated for each point in the image cube by randomly generating lines in the N-dimensional space comprising a scatterplot of the MNF transformed data. All of the points in the space are now projected onto the lines and those ones that fall at the extremes of the lines are counted. After many repeated projections to different lines, those pixels that count above a certain threshold are declared “pure”. These potential endmember spectra are loaded into an Ndimensional visualization tool and rotated in real time until extremities in the data cloud that will likely correspond with scene endmembers are visually identified.
Hyperspectral Data Classification
There are many techniques developed for extracting extensive information contained in hyperspectral data Most of these algorithms Spectral analysis methods usually compare pixel spectra with a reference (or target) spectrum. Target spectra can be derived from a variety of sources, including spectral libraries, regions of interest within a spectral image, or individual pixels within a spectral image. The most commonly used method for information extraction using hyperspectral data are
Per Pixel Classification Methods
The Per pixel classification methods attempt to determine the abundances of one or more target materials within each pixel in a hyperspectral data on the basis of the spectral similarity between the pixel and target spectra. These methods include standard supervised classifiers such as Minimum Distance or Maximum Likelihood and classifiers developed specifically for classifying hyperspectral data such as Spectral Angle Mapper and Spectral Feature Fitting.
Spectral Angle Mapper Classification
SAM is an automated method for comparing image spectra to individual spectra or to a spectral library (Boardman, unpublished data; CSES, 1992; Kruse et al., 1993a). SAM assumes that the data have been reduced to apparent reflectance (true reflectance multiplied by some unknown gain factor, controlled by topography and shadows). The algorithm determines the similarity between two spectra by calculating the spectral angle between them, treating them as vectors in n-D space, where n is the number of bands. SAM considers every pixel in the scene and evaluates the similarity of the spectra to repress the influence of the shading, which accentuates the characteristics of reflectance. The image spectrum is then assigned a correlation factor between 0 (low correlation) and 1 (high correlation) and compared to a spectral library or endmember. With SAM, the data are converted to apparent reflectance, which is the true reflectance with gain coefficients that are defined by terrain and lighting conditions.Consider a reference spectrum and an unknown spectrum from two-band data. The two different materials are represented in a 2D scatter plot by a point for each given illumination, or as a line (vector) for all possible illuminations. Because SAM uses only the direction of the spectra, not the length, SAM is insensitive to the unknown gain factor. All possible illuminations are treated equally. Poorly illuminated pixels fall closer to the origin of the scatter plot. The color of a material is defined by the direction of its unit vector. The angle between the vectors is the same, regardless of the length. The length of the vector relates only to how fully the pixel is illuminated. The SAM algorithm generalizes this geometric interpretation to n-D space. SAM determines the similarity of an unknown spectrum t to a reference spectrum r, by applying the following equation:
∝=cos^(-1)[(∑_(i=1)^nb▒〖t_i r_i 〗)/■({∑_(i=1)^nb▒t_i^2 }^(1/2)&{∑_(i=1)^nb▒r_i^2 }^(1/2) )]
where nb equals the number of bands in the image.
The spectral angle is the angle between any two vectors originating from a common origin. The magnitude of the angle indicates the similarity or dissimilarity of the materials—a smaller angle correlates to a more similar spectral signature. This method is relatively insensitive to changes in illumination on the target material because changes in light will impact the magnitude but not the direction of the vector. A poorly illuminated target will cause the points to be plotted closer to the origin.
Sub-Pixel Classification:
Sub-pixel analysis methods can be used to calculate the quantity of target materials in each pixel of an image. Sub-pixel analysis can detect quantities of a target that are much smaller than the pixel size itself. In cases of good spectral contrast between a target and its background, sub-pixel analysis has detected targets covering as little as 1-3% of the pixel. Sub-pixel analysis methods include Complete Linear Spectral Unmixing, and Matched Filtering.
Linear Spectral Unmixing
Linear Spectral Unmixing is a means of determining the relative abundances of materials depicted in multispectral imagery based on the material’s spectral characteristics. The reflectance at each pixel of the image is assumed to be a linear combination of the reflectance of each material (or endmember) present within the pixel. There are certain limitations that apply for the linear spectral unmixing technique. The number of endmembers must be less than the number of spectral bands and all of the endmembers in the image must be used for an efficient mapping result. Spectral unmixing results are highly dependent on the input endmembers and changing the endmembers will change the results.
Unmixing simply solves a set of n linear equations for each pixel, where n is the number of bands in the image. The unknown variables in these equations are the fractions of each endmember in the pixel. To be able to solve the linear equations for the unknown pixel fractions it is necessary to have more equations than unknowns, which means that we need more bands than endmember materials. With hyperspectral data this is almost always true. The results of Linear Spectral Unmixing include one abundance image for each endmember. The pixel values in these images indicate the percentage of the pixel made up of that endmember. For example, if a pixel in an abundance image for the endmember quartz has a value of 0.90, then 90% of the area of the pixel contains quartz. An error image is also usually calculated to help evaluate the success of the unmixing analysis.
Mixture tuned matched filtering
Spectral Feature Fitting
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