A superior edge preserving filter with a systematic analysis

A new, adaptive, edge preserving filter for use in image processing is presented. It had superior performance when compared to other filters. Termed the contiguous K-average, it aggregates pixels by examining all pixels contiguous to an existing cluster and adding the pixel closest to the mean of the existing cluster. The process is iterated until K pixels were accumulated. Rather than simply compare the visual results of processing with this operator to other filters, some approaches were developed which allow quantitative evaluation of how well and filter performs. Particular attention is given to the standard deviation of noise within a feature and the stability of imagery under iterative processing. Demonstrations illustrate the performance of several filters to discriminate against noise and retain edges, the effect of filtering as a preprocessing step, and the utility of the contiguous K-average filter when used with remote sensing data

Multilayer MIM inversion of AEM data: Theory and field example

This paper presents a multilayer generalization of an algebraic method of inverting frequency-doma in airborne active electromagnetic (AEM) data in terms of 1-D layered earth models. The processing of the AEM data, which includes a recalibration procedure, is also outlined. The inversion is applied to synthetic fields generated from a multilayer model which is intended to approximate a measured conductivity profile of the water column in the Gulf of Mexico and to measured AEM data from a survey of the Barataria Bay estuary region of the Louisiana Gulf of Mexico coast. The inversion results from the synthetic data are in good agreement with the forward model. The conductivities calculated from the inversions of measured AEM data are compared to ground-and water-based measurements. The depth variations of the calculated electrical conductivities in the nearshore Gulf waters are in good agreement with measurements of conductivity versus depth by conductivity-temperature-depth (CTD) casts at several points on the over-the-water portion of two flight lines. ©2001 Society of Exploration Geophysicist

MIM and nonlinear least-squares inversions of AEM data in Barataria basin, Louisiana

An airborne electromagnetic survey was performed over the marsh and estuarine waters of the Barataria basin of Louisiana. Two inversion methods were applied to the measured data to calculate layer thicknesses and conductivities: the modified image method (MIM) and a nonlinear least-squares method of inversion using two two-layer forward models and one three-layer forward model, with results generally in good agreement. Uniform horizontal water layers in the near-shore Gulf of Mexico with the fresher (less saline, less conductive) water above the saltier (more saline, more conductive) water can be seen clearly. More complex near-surface layering showing decreasing salinity/conductivity with depth can be seen in the marshes and inland areas. The first-layer water depth is calculated to be 1–2 m, with the second-layer water depth around 4 m. The first-layer marsh and beach depths are computed to be 0–3 m, and the second-layer marsh and beach depths vary from 2 to 9 m. The first-layer water conductivity is calculated to be 2–3 S/m, with the second-layer water conductivity around 3 to 4 S/m and the third-layer water conductivity 4–5 S/m. The first-layer marsh conductivity is computed to be mainly 1–2 S/m, and the second- and third-layer marsh conductivities vary from 0.5 to 1.5 S/m, with the conductivities decreasing as depth increases except on the beach, where layer three has a much higher conductivity, ranging up to 3 S/m. ©2003 Society of Exploration Geophysicist

MIM and nonlinear least-squares inversions of AEM data in Barataria basin, Louisiana

An airborne electromagnetic survey was performed over the marsh and estuarine waters of the Barataria basin of Louisiana. Two inversion methods were applied to the measured data to calculate layer thicknesses and conductivities: the modified image method (MIM) and a nonlinear least-squares method of inversion using two two-layer forward models and one three-layer forward model, with results generally in good agreement. Uniform horizontal water layers in the near-shore Gulf of Mexico with the fresher (less saline, less conductive) water above the saltier (more saline, more conductive) water can be seen clearly. More complex near-surface layering showing decreasing salinity/conductivity with depth can be seen in the marshes and inland areas. The first-layer water depth is calculated to be 1–2 m, with the second-layer water depth around 4 m. The first-layer marsh and beach depths are computed to be 0–3 m, and the second-layer marsh and beach depths vary from 2 to 9 m. The first-layer water conductivity is calculated to be 2–3 S/m, with the second-layer water conductivity around 3 to 4 S/m and the third-layer water conductivity 4–5 S/m. The first-layer marsh conductivity is computed to be mainly 1–2 S/m, and the second- and third-layer marsh conductivities vary from 0.5 to 1.5 S/m, with the conductivities decreasing as depth increases except on the beach, where layer three has a much higher conductivity, ranging up to 3 S/m. ©2003 Society of Exploration Geophysicist

Characteristic polynomials of distance matrices of one dimensional sets

AbstractProperties of the eigenvalues of the distance matrix of a one dimensional point set are derived from identities involving the characteristic polynomial and some related polynomials called the Ant, Sym, Din and Sof polynomials of the point set. Let A⊕B denote the concatenation of the lists A and B and MS[i,j]=M[m+1-i,n+1-j] the spin of the m by n matrix M. The Ant and Sym polynomials come from a factorization of the characteristic polynomial of the distance matrix of the set -AS⊕A obtained by reflecting A about the origin. The roots of Ant are the eigenvalues with antisymmetric eigenvectors and the roots of Sym are the eigenvalues with symmetric eigenvectors. Given a square matrix M and a vector A, we say that v≠0 is an eigenvector of M relative to A iff Mv=λv+kA and A·v=0. Some basic properties of relative eigenvectors are developed. The roots of Din are the eigenvalues of the distance matrix of A relative to the vector of 1’s and the roots of Sof are the eigenvalues relative to A itself. Some simple recursions for these polynomials obtained using expansion by minors are elaborated into an extensive series of identities relating polynomials of lists to polynomials of concatenations of the lists. These identities are then used to derive a linear time algorithm for computing the polynomials and proving some results about location, distinctness and interlacing of eigenvalues

Multilayer MIM inversion of AEM data: Theory and field example

This paper presents a multilayer generalization of an algebraic method of inverting frequency-doma in airborne active electromagnetic (AEM) data in terms of 1-D layered earth models. The processing of the AEM data, which includes a recalibration procedure, is also outlined. The inversion is applied to synthetic fields generated from a multilayer model which is intended to approximate a measured conductivity profile of the water column in the Gulf of Mexico and to measured AEM data from a survey of the Barataria Bay estuary region of the Louisiana Gulf of Mexico coast. The inversion results from the synthetic data are in good agreement with the forward model. The conductivities calculated from the inversions of measured AEM data are compared to ground-and water-based measurements. The depth variations of the calculated electrical conductivities in the nearshore Gulf waters are in good agreement with measurements of conductivity versus depth by conductivity-temperature-depth (CTD) casts at several points on the over-the-water portion of two flight lines. ©2001 Society of Exploration Geophysicist