Iterative Error Analysis Research Articles

A Retrieval Method of Effective Electromagnetic Parameters for Inhomogeneous Metamaterials

In this paper, we develop a method to extract effective electromagnetic parameters of inhomogeneous metamaterials. Starting with a two-layer inhomogeneous structure, the relationship between S-parameters and effective electromagnetic parameters of each layer, including wave impedance and refractive index, is derived. A recursion procedure in terms of S-parameters is developed to deal with an m-layer inhomogeneous structure. To ensure consistency and correctness of the retrieved electromagnetic parameters, an iterative solution procedure is proposed. An iterative error analysis is given to show that with the increase of iterative steps, the resulting error is accumulated. Therefore, a direct solution approach based on nonlinear equation systems is developed. Several inhomogeneous examples, including material and metamaterial structures, are given to demonstrate validity, feasibility, and noise insensitivity of the proposed method.

Distributed Parallel Endmember Extraction of Hyperspectral Data Based on Spark

Due to the increasing dimensionality and volume of remotely sensed hyperspectral data, the development of acceleration techniques for massive hyperspectral image analysis approaches is a very important challenge. Cloud computing offers many possibilities of distributed processing of hyperspectral datasets. This paper proposes a novel distributed parallel endmember extraction method based on iterative error analysis that utilizes cloud computing principles to efficiently process massive hyperspectral data. The proposed method takes advantage of technologies including MapReduce programming model, Hadoop Distributed File System (HDFS), and Apache Spark to realize distributed parallel implementation for hyperspectral endmember extraction, which significantly accelerates the computation of hyperspectral processing and provides high throughput access to large hyperspectral data. The experimental results, which are obtained by extracting endmembers of hyperspectral datasets on a cloud computing platform built on a cluster, demonstrate the effectiveness and computational efficiency of the proposed method.

IEA(Iterative Error Analysis)와 분광혼합분석기법을 이용한 초분광영상의 변화탐지

Various algorithms such as Chronochrome (CC), Principle Component Analysis (PCA), and spectral unmixing have been studied for hyperspectral change detection. Change detection by spectral unmixing offers useful information on the nature of the change compared to the other change detection methods which provide only the locations of changes in the scene. However, hyperspectral change detection by spectral unmixing is still in an early stage. This research proposed a new approach to extract endmembers, which have identical properties in temporally different images, by Iterative Error Analysis (IEA) and Spectral Angle Mapper (SAM). The change map obtained from the difference of abundance efficiently showed the changed pixels. Simulated images generated from Compact Airborne Spectrographic Imager (CASI) and Hyperion were used for change detection, and the experimental results showed that the proposed method performed better than CC, PCA, and spectral unmixing using N-FINDR. The proposed method has the advantage of automatically extracting endmembers without prior information, and it could be applicable for the real images composed of many materials.

Automatic extraction of optimal endmembers from airborne hyperspectral imagery using iterative error analysis (IEA) and spectral discrimination measurements.

Pure surface materials denoted by endmembers play an important role in hyperspectral processing in various fields. Many endmember extraction algorithms (EEAs) have been proposed to find appropriate endmember sets. Most studies involving the automatic extraction of appropriate endmembers without a priori information have focused on N-FINDR. Although there are many different versions of N-FINDR algorithms, computational complexity issues still remain and these algorithms cannot consider the case where spectrally mixed materials are extracted as final endmembers. A sequential endmember extraction-based algorithm may be more effective when the number of endmembers to be extracted is unknown. In this study, we propose a simple but accurate method to automatically determine the optimal endmembers using such a method. The proposed method consists of three steps for determining the proper number of endmembers and for removing endmembers that are repeated or contain mixed signatures using the Root Mean Square Error (RMSE) images obtained from Iterative Error Analysis (IEA) and spectral discrimination measurements. A synthetic hyperpsectral image and two different airborne images such as Airborne Imaging Spectrometer for Application (AISA) and Compact Airborne Spectrographic Imager (CASI) data were tested using the proposed method, and our experimental results indicate that the final endmember set contained all of the distinct signatures without redundant endmembers and errors from mixed materials.

수정된 IEA 기반의 분광혼합분석 기법을 이용한 임상분류

분광혼합분석 결과로 얻어지는 각 물체의 점유비율을 활용하면 보다 세밀한 분류가 가능하다. 이는 복잡한 도심지역의 피복분류 뿐만 아니라 혼효림이 많은 한반도 임상분류에 적합한 분류기법이 될 수 있다. 효과적인 임상분류를 위해서는 무엇보다 적절한 endmember의 추출이 선행되어야 하는데, 기존에 주로 사용되었던 기하학적 방법(geometric endmember selection)은 분광특성이 유사한 산림지역에 적합하지 않다. 본 연구에서는 영상에서 직접 순수한 화소를 추출하는 기법 중의 하나인 IEA(Iterative Error Analysis)와 침엽수와 활엽수의 분광특성을 이용하여 실험지역을 대표할 수 있는 각각의 endmember를 자동으로 추출하였다. CASI(Compact Airborne Spectrographic Imager) 영상의 두 지역에 대하여 분광혼합분석을 이용한 분류를 수행한 결과, 분류 정확도는 각각 86%와 90%로, 제안한 기법이 실험대상지역을 대표하는 침엽수와 활엽수의 endmember를 적절하게 추출한 것으로 나타났다. 분광혼합분석 기법을 이용한 보다 효과적인 분류를 위해서 분류항목 외 기타물질을 endmember로 고려하는 연구가 필요할 것으로 보인다. Fractional values resulted from the spectral mixture analysis could be used to classify not only urban area with various materials but also forest area in more detailed spatial scale. Especially South Korea is largely consist of mixed forest, so the spectral mixture analysis is suitable as a classification method. For the successful classification using spectral mixture analysis, extraction of optimal endmembers is prerequisite process. Though geometric endmember selection has been widely used, it is barely suitable for forest area. Therefore, in this study, we modified Iterative Error Analysis (IEA), one of the most famous algorithms of image endmember selection which extracts pure pixel directly from the image. The endmembers which represent deciduous and coniferous trees are automatically extracted. The experiments were implemented on two sites of Compact Airborne Spectrographic Imager (CASI) and classified forest area into two types. Accuracies of each classification results were 86% and 90%, which mean proposed algorithm effectively extracted proper endmembers. For the more accurate classification, another substances like forest gap should be considered.

A Hybrid Automatic Endmember Extraction Algorithm Based on a Local Window

Anomaly endmembers play an important role in the application of remote sensing, such as in unmixing classification and target detection. Inspired by the iterative error analysis (IEA), a hybrid endmember extraction algorithm (HEEA) based on a local window is proposed in this paper, which focuses on improving the accuracy of endmember extraction. HEEA uses the spectral-information-divergence-spectral-angle-distance metric to measure the similarity and the orthogonal subspace projection (OSP) method to search for the endmembers, which can decrease the correlation between extracted endmember spectra. Moreover, it is based on a local window which integrates both spatial and spectral aspects to extract endmembers. A synthetic image and Airborne Visible/Infrared Imaging Spectrometer data were tested with the HEEA method, classical IEA, OSP, simplex growing algorithm, sequential maximum angle convex cone, and spectral spatial endmember extraction automatic endmember extraction method. Experimental results indicated that HEEA manifested a slightly better improvement in the rmse and spectrum information than the other methods. The effect was investigated with various SNRs and different window sizes. The robustness of HEEA is better than the classical IEA, even with lower SNR.

Remote predictive lithologic mapping in the Abitibi Greenstone Belt, Canada, using airborne hyperspectral imagery

This study reports an attempt to conduct remote predictive lithologic mapping in the Abitibi Greenstone Belt near Noranda, Quebec, an area characterized by a low abundance of rock outcrop and a predominance of vegetation. Where impeding vegetation is dominant and bedrock exposure is minimal, end-member spectra for the important map units (basalt, rhyolite, diorite, and granite) could not be identified by means of pixel purity index (PPI) and iterative error analysis (IEA) end-member search tools. These tools did not appear to be of practical use for scenes where vegetation is dominant and bedrock exposure is minimal. Field spectral measurements were performed to document bedrock and vegetal hyperspectral characteristics and determine the diversity of dominant lithologic units. These results were used to guide the development of a method for geologic mapping using airborne hyperspectral data. Data analysis was performed by means of spectral mixture analysis, and the resulting predictive map was compared with the known geological map. Despite the effect of variable lichen cover, the predictive map compares well with the known lithologic distributions of diorite, basalt, and rhyolite. The predicted distribution of granite is complicated by the spectral similarity with felsic volcanics in parts of the map area. The distribution of rhyolite was mapped with acceptable accuracy, a significant result for mineral exploration in that rhyolite is the main host to mineralization in the Abitibi belt.

A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations

We revisit a fast iterative method studied by us in [I.K. Argyros, On a two-point Newton-like method of convergent order two, Int. J. Comput. Math. 88 (2) (2005) 219–234] to approximate solutions of nonlinear operator equations. The method uses only divided differences of order one and two function evaluations per step. This time we use a simpler Kantorovich-type analysis to establish the quadratic convergence of the method in the local as well as the semilocal case. Moreover we show that in some cases our method compares favorably, and can be used in cases where other methods using similar information cannot [S. Amat, S. Busquier, V.F. Candela, A class of quasi-Newton generalized Steffensen's methods on Banach spaces, J. Comput. Appl. Math. 149 (2) (2002) 397–406; D. Chen, On the convergence of a class of generalized Steffensen's iterative procedures and error analysis, Int. J. Comput. Math. 31 (1989) 195–203]. Numerical examples are provided to justify the theoretical results.

Parallel Implementation of Endmember Extraction Algorithms From Hyperspectral Data

Automated extraction of spectral endmembers is a crucial task in hyperspectral data analysis. In most cases, the computational complexity of endmember extraction algorithms is very high, in particular, for very high-dimensional datasets. However, the intrinsic properties of available techniques are amenable to the design of parallel implementations. In this letter, we evaluate several parallel algorithms that represent three representative approaches to the problem of extracting endmembers. Two parallel algorithms have been selected to represent a first class of algorithms based on convex geometry concepts. In particular, we develop parallel implementations of approximate versions of the N-FINDR and pixel purity index algorithms, along with a parallel hybrid of both techniques. A second class is given by algorithms based on constrained error minimization and represented by a parallel version of the iterative error analysis algorithm. Finally, a parallel version of the automated morphological endmember extraction algorithm is also presented and discussed. This algorithm integrates the spatial and spectral information as opposed to the other discussed algorithms, a feature that introduces additional considerations for its parallelization. The proposed algorithms are quantitatively compared and assessed in terms of both endmember extraction accuracy and parallel efficiency, using standard AVIRIS hyperspectral datasets. Performance data are measured on Thunderhead, a parallel supercomputer at NASA's Goddard Space Flight Center

MA57---a code for the solution of sparse symmetric definite and indefinite systems

We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of the implementation details and emphasize the novel features of MA57. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom.

Atmospheric effects on the classification of surface minerals in an arid region using Short-Wave Infrared (SWIR) hyperspectral imagery and a spectral unmixing technique

This study focuses on the comparison of spectral unmixing results from at-sensor radiance data and atmospherically corrected data, i.e., surface reflectance. The airborne Short-Wave Infrared (SWIR) Full Spectrum Imager (SFSI) and Airborne Visible and Infrared Imaging Spectrometer (AVIRIS) were used to acquire data over Cuprite, Nevada, in June 1995 and 1996, respectively. This is an arid region that is well known for its exposed bedrock and alteration zones. For this project, a portion of the SWIR-2 spectral range covering the atmospheric window between 2050 and 2350 nm and a linear spectral unmixing technique were used to map surface minerals, including products of hydrothermal alteration. In total, eight end-members were extracted from the imagery using a new automatic procedure called Iterative Error Analysis (IEA). The atmospheric corrections were applied using a look-up-table procedure implemented in the Imaging Spectrometer Data Analysis System (ISDAS) and created with the radiative transfer model MODTRAN3. The fraction, or abundance, maps derived from the two types of data were compared using the coefficient of determination (R2) and the Average Euclidean Distance Coefficient (AEDC). Very good unmixing agreement was found between the results from the at-sensor radiance data and those from the surface reflectance data. For the SFSI data, the R2 values range from 0.72 to 0.95 and the AEDC values range from 0.098 to 0.023, whereas for the AVIRIS data, the R2 values range from 0.92 to 0.99 and the AEDC values range from 0.021 to 0.008. This suggests that, for the spectral range considered, atmospheric corrections are not necessary for mineral mapping in an arid region and for desert atmospheric conditions.

133Cs Chemical Shielding Anisotropies and Quadrupole Couplings from Magic-Angle Spinning NMR of Cesium Salts

Magnitudes and relative orientations of 133Cs quadrupole coupling and chemical shielding tensors have been accurately determined from 133Cs magic-angle spinning (MAS) NMR spectra of the central and satellite transitions for four powdered cesium salts. Effects of small 133Cs chemical shielding anisotropies on the spectral appearance are observed in highly stabilized low-speed 133Cs MAS NMR spectra and analyzed by iterative fitting and numerical error analysis of the complete manifolds of spinning sidebands. 133Cs MAS NMR spectra of the single Cs site for CsVO3 and CsClO4, recorded at different spinning speeds, give consistent values for the parameters describing the two tensor interactions, while numerical error analysis of the spectra demonstrates that high levels of accuracy can be obtained for all parameters employing low-speed MAS NMR. The performance of the method for powders containing multiple sites is demonstrated by the 133Cs MAS spectra of Cs2CrO4 and Cs2SO4. The error limits for the 133Cs MAS NMR data for Cs2CrO4 are similar to those reported in a recent single-crystal NMR study. Quadrupole coupling parameters and isotropic chemical shifts are reported for Cs2CO3 from a high-speed 133Cs MAS spectrum. A linear correlation between 133Cs quadrupole tensor elements and estimated EFG tensor elements from point-charge calculations, employing effective oxygen charges, is reported and used to assign the NMR parameters for the two different crystallographic sites in Cs2CrO4, Cs2SO4, and Cs2CO3.

On the convergence of a class of generalized steffensen's iterative procedures and error analysis

We consider a class of generalized Steffensen's methods for solving nonlinear equations without any derivative. We establish successful the existence-convergence theorem of generalized Steffensen's iteration under the Kantorovich-Ostrowski's conditions and present an upper bound, but it is not optimal. These conclusions contain the special case of Steffensen's method [6]. In the mean time, we compare the accurate error bound of Newton's method with error bounds of generalized Steffensen's methods, we show that latter is less than former.