Spectral Unmixing Applied to Desert Soils for the - Naval ...

More documents

Recommendations

Info

where: is the mean corrected and noise whitened result is the diagonal matrix with elements being a square root of the reciprocal to the noise eigenvalues is the nb, nb matrix of noise eigenvectors with nb being the number of bands is the original data set as a number of pixels, number of bands matrix is set as the mean value of a band j of The goal of step two is use of the calculated matched filter along with the minimum noise fraction (MNF) to estimate target abundances on a sub-pixel level. With the final MNF output (Dmnf) being calculated using equation (8) from Boardman and Kruse (2011). where: is the MNF data, represents the diagonal covariance structure containing MNF eigenvalues that are equivalent to the covariance values, is the principal component transform result from the data that has been both mean corrected and noise whitened. The MNF data have a zero mean and uncorrelated unit variance white noise that, when projected onto their eigenvectors, yield a diagonal covariance structure. The covariance values are equal to the MNF eigenvalues and are the base by which MTMF processing then occurs (Boardman and Kruse, 2011). When a pixel is filled with certain materials, the degree of spectral variability is reduced simultaneously. If the pixel is filled to 50% with that material, one encounters 44 (7) (8)
the situation where mixing freedom within the pixel is halfway between the background- plus-noise freedom of a 0% filled pixel and the noise-only-freedom of the pixel filled to 50% (Boardman and Kruse, 2011). It is this concept that allows the MTMF process to identify false positives by placing pixels well outside their plausible mixing freedom into an infeasible mixtures category. Finally, MTMF creates a distribution range for feasible mixtures (Boardman and Kruse, 2011). Further details on the mathematics behind this process are given in the paper by Boardman and Kruse (2011). The MNF process revealed that the eigenvalues for the AVIRIS f110512t01p00r07 flight log drop to 1 at approximately eigenvalue band 49, which means that the bands after eigenvalue band 49 contain mainly noise. Based on this, the data were then reduced from the initial 207 bands used to using only the first 50 bands in steps after the MNF process in order to eliminate noise from the data and providing a new dimensionality of 50 (Figure 22). Figure 22. The plot (A) shows that the eigenvalues calculated for the image drop toward 1 at approximately eigenvalue band 50, meaning that most of the data in this band is noise. The bottom figure (B) is a visualization of eigenvalue band 50, confirming that though there is some signal present, band 50 is dominated by noise. As an example of the Pixel Purity Index (PPI) calculation using the f110512t01p00r07 data set, the number of PPI iterations was set at the default setting of 5,000 iterations, and a PPI threshold value of 2.5. The resulting plot can be seen in Figure 23. When looking at the plot, the curve flattens off at around 2000 iterations, so the index was run a second time with 3000 iterations because 5000 seemed unnecessary. The lower iteration plot can 45
Page 1 and 2:
NAVAL POSTGRADUATE SCHOOL MONTEREY,
Page 3 and 4:
REPORT DOCUMENTATION PAGE Form Appr
Page 5 and 6:
Approved for public release; distri
Page 7 and 8:
ABSTRACT Desert areas cover approxi
Page 9 and 10:
TABLE OF CONTENTS I. INTRODUCTION..
Page 11 and 12:
LIST OF FIGURES Figure 1. The above
Page 13 and 14: spectrum by atmospheric effects. Re
Page 15 and 16: emoved function showing an absorpti
Page 17 and 18: LIST OF TABLES Table 1. This table
Page 19 and 20: LIST OF ACRONYMS AND ABBREVIATIONS
Page 21 and 22: I. INTRODUCTION A study published b
Page 23 and 24: II. THE PHYSICS BEHIND REMOTE SENSI
Page 25 and 26: sensitive a given sensor is to diff
Page 27 and 28: Figure 3. From Green et al. (1998),
Page 29 and 30: analyzing imagery spectra, it is mo
Page 31 and 32: After data have been converted to r
Page 33 and 34: Collins et al. (1997) was able to s
Page 35 and 36: These purposes include, but are not
Page 37 and 38: III. DESERT ECOSYSTEM CHARACTERISTI
Page 39 and 40: sagebrush of Utah, Montana, and the
Page 41 and 42: in desert regions include argids, o
Page 43 and 44: 2. Biological Soil Crusts (BSCs) Bi
Page 45 and 46: 2004), especially in cases where ma
Page 47 and 48: IV. STUDY SITES The focus area of t
Page 50 and 51: Figure 13. This figure illustrates
Page 52 and 53: Following the uplift that occurred
Page 54 and 55: the Mazourka Canyon OHV park betwee
Page 56 and 57: wavelengths being analyzed to obtai
Page 58 and 59: 2. Field Spectroscopy An Analytical
Page 60 and 61: A spectral library was then built a
Page 62 and 63: after atmospherically correcting th
Page 66 and 67: also be seen in Figure 23. The leve
Page 68 and 69: Figure 24. This figure is a compari
Page 70 and 71: Figure 25. This figure shows ASD co
Page 72 and 73: Looking at Figure 25 it is apparent
Page 74 and 75: A. IMAGERY DERIVED ENDMEMBERS The i
Page 76 and 77: Figure 28. The above shows some of
Page 78 and 79: spectrometer, reflectance values we
Page 80 and 81: such an inference can be made (Ben-
Page 82 and 83: While this is lower than the hoped
Page 84 and 85: While the lower value would initial
Page 86 and 87: Figure 33. This figure shows the ad
Page 88 and 89: Inset C of Figure 35 is the same da
Page 90 and 91: However, the presences of BSCs are
Page 92 and 93: A B C Figure 37. Inset A shows the
Page 94 and 95: A B C Figure 38. Inset A shows a co
Page 96 and 97: differences in the studies by other
Page 98 and 99: small concentrations making them un
Page 100 and 101: area making it possible to tell wha
Page 102 and 103: Clark, R. N., Swayze, G. A., Livo,
Page 104 and 105: Kruse, F. A., Boardman, J. W., and
Page 106 and 107: Sharp, R. P., and Glazner, A. F., (
Page 108: INITIAL DISTRIBUTION LIST 1. Defens
show all

Spectral Unmixing Applied to Desert Soils for the - Naval ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?