Andy Green

A transformation for ordering multispectral data in terms of image quality with implications for noise removal

A transformation known as the maximum noise fraction (MNF) transformation, which always produces new components ordered by image quality, is presented. It can be shown that this transformation is equivalent to principal components transformations when the noise variance is the same in all bands and that it reduces to a multiple linear regression when noise is in one band only. Noise can be effectively removed from multispectral data by transforming to the MNF space, smoothing or rejecting the most noisy components, and then retransforming to the original space. In this way, more intense smoothing can be applied to the MNF components with high noise and low signal content than could be applied to each band of the original data. The MNF transformation requires knowledge of both the signal and noise covariance matrices. Except when the noise is in one band only, the noise covariance matrix needs to be estimated. One procedure for doing this is discussed and examples of cleaned images are presented. >

Airborne electromagnetics — Providing new perspectives on geomorphic process and landscape development in regolith-dominated terrains

Abstract In regolith-dominated terrains, the nature of contemporary processes and the surface distribution of regolith materials may be a poor guide to the character and history of regolith materials at depth. The nature of regolith materials at depth is often critical to unravelling the development of a landscape. Conventional mapping aids such as air photos, multispectral remote sensing and airborne radiometrics are not wholly adequate in this context, as they penetrate limited depths ( 100m). The application of AEM to regolith mapping and its potential as a tool in geomorphology are illustrated by reference to an AEM survey flown at Lawlers in the Yilgarn Craton of Western Australia. At Lawlers, AEM identifies a palaeochannel that has no surface expression. It cannot be seen in images of the Landsat, airborne radiometric or airborne magnetic data. The disposition of this channel in the landscape, and in particular its association with ferruginous materials forming breakaways, suggest that inversion of relief has been a significant factor in the evolution of the Lawlers landscape. The AEM data at Lawlers have also been used to map the weathering front. The topography of the weathering front not only reflects the movement of water through the landscape in a general sense, but also reflects the influence of lithology and structure. Different lithologies are clearly weathering to different depths. Information on the nature of the weathering front is potentially an important constraint on models of groundwater flow, and by association, models of solute dispersion.

Estimating band-to-band misregistrations in aliased imagery

Abstract We compare two classes of techniques, cross-covariance-based and Fourier-based, for estimating band-to-band misregistrations in multispectral imagery. We show that both methods often give biased estimates of the misregistrations, the former because of inadequate interpolation procedures and the latter because they do not account for the presence of aliasing. Such aliasing is often present, especially in remote sensing imagery. We describe a Fourier-based method that accounts for aliasing and that, for a variety of 512 × 512 image pairs, gives misregistration estimates with standard errors quite often less than 1/100th of a pixel in both horizontal and vertical directions. The theory is applied to one artificial and three real image pairs, thus demonstrating some of its practical consequences. There is also a brief discussion of the implications of the theory for image registration.

Mid-Infrared Remote Sensing Systems and Their Application to Lithologic Mapping

Mid-infrared remote lithologic mapping by emittance and by reflectance are assessed in laboratory experiments. The emittance spectra of various rocks and minerals, measured in the 8-13, ¿m atmospheric transmission window, are compared with reflectance data measured in the range of 9.2-11.2 Am using a line-tuned CO2 laser. We conclude that the reflectance data are more useful for lithologic discrimination than the passive emittance data. An experimental laser suitable for terrain mapping from a low-flying aircraft is described. The low-pressure longitudinal discharge CO2 laser has a rotating mirror to scan the diffraction grating and generates 90 bursts of pulses per second. Each 1-ms burst contains 92 pulses at 92 CO2 laser wavelengths. The mean output power is 12 W and the average pulse power is 370 W. With that power, and using incoherent detection, a signal-to-noise ratio of better than 100: 1 should be obtained from terrain with an albedo of 0.01 at a height of 500 m.

A Comparison Between Three Sparse Unmixing Algorithms Using a Large Library of Shortwave Infrared Mineral Spectra

The comparison described in this paper has been motivated by two things: 1) a “spectral library” of shortwave infrared reflectance spectra that we have built, consisting of the spectra of 60 nominally pure materials (mostly minerals, but also water, dry vegetation, and several man-made materials) and 2) the needs of users in the mining industry for the use of fast and accurate unmixing software to analyze tens to hundreds of thousands of spectra measured from drill core or chips using HyLogging instruments, and other commercial reflectance spectrometers. Individual samples are typically a mixture of only one, two, three, or occasionally four minerals. Therefore, in order to avoid overfitting, a sparse unmixing algorithm is required. We compare three such algorithms using some real world test data sets: full subset selection (FSS), sparse demixing (SD), and L1 regularization. To aid the comparison, we introduce two novel aspects: 1) the simultaneous fitting of the low frequency background with mineral identification (which provides greater model flexibility) and 2) the combined fitting being carried out using a suitably defined Mahalanobis distance; this has certain optimality properties under an idealized model. Together, these two innovations significantly improve the accuracy of the results. FSS and L1 regularization (suitably optimized) produce similar levels of accuracy, and are superior to SD. Discussion includes possible improvements to the algorithms, and their possible use in other domains.