Maximum Noise Fraction Research Articles

Filtering high-resolution hyperspectral imagery in a maximum noise fraction transform domain using wavelet-based de-striping

Ever improving technology and computer processing power and decreasing cost have made hyperspectral image acquisition and analysis affordable in many applications. Hyperspectral images, acquired normally using pushbroom sensing systems, are tainted with noise and nonperiodic stripes. Few methods, including wavelet-based ones, have been proposed for reducing nonperiodic stripes from multispectral images; there are even fewer studies dealing with nonperiodic stripes in high-resolution hyperspectral images. Applying de-striping filters directly to individual hyperspectral image bands can be computationally inefficient and complicated considering the large number of bands in this type of image. This article compares the performance of wavelet-based de-striping algorithms as applied on high-resolution hyperspectral imagery. The algorithms are implemented directly on individual bands in the image domain and on selected bands in the image maximum noise fraction (MNF) transform domain. Two wavelet-based de-striping algorithms were tested and compared. The first algorithm eliminates wavelet detail components in the striping direction, while the second algorithm adaptively filters these components. The filtering methods are evaluated through visual and quantitative assessments. Quantitative assessment is performed by analysing the autocorrelation coefficient and signal-to-noise-ratio. The results show that images filtered in the MNF domain are superior in reducing stripes and noise while retaining the image information and without introducing distortions. The technique is computationally effective through filtering fewer bands, which reduces the need for filtering parameter determination and fine tuning. Visual and quantitative assessments also show that adaptive filtering of wavelet components is better than eliminating entire components due to the retention of image content.

Application of PCA-CFAR-MNF to Image Enhancement for a UGV FLGPR

The UGV (Unmanned Ground Vehicle) FLGPR (Forward-Looking Ground Penetrating Radar) imaging model spatially variable characteristics lead to the relatively low image SCR (Signal-Clutter Ratio). In order to improve the image quality and improve the SCR, the coherence properties of the target in image sequences is used for image enhancement. That is, images from the same region at different time sequence are enhanced two times. First of all, CFAR (Constant False Alarm Rate) is a preliminary step to enhance the image sequence, and then PCA-CFAR-MNF enhancement algorithm is proposed: according to the iterative nature of the MNF (Maximum Noise Fraction), PCA (Principal Component Analysis) method is first used to transform selecting and then CFAR detection is used to estimate the image background in the iteration,. The measured data show that the proposed method not only keeping the target characteristics, but also have remarkable image enhancement effect, and have greatly improved SCR.

Comparison of Processing Chains Based on Support Vector Machine Classifier for Hyperspectral Image Classification

In this research, we compared the performance of different processing chains resulting from combinations of spatial denoising filters, unsupervised feature transformation methods, and a support vector machine classifier. Two different training and test sample scenarios were investigated and conducted on an AVIRIS image over the Indian Pines region in Indiana, USA. The results showed that by using the process chain (adaptive enhanced Lee filter, maximum noise fraction, and support vector machine) the classification accuracies of the kappa coefficient were better than those of the best previously published techniques.

Linear and kernel methods for multivariate change detection

The iteratively reweighted multivariate alteration detection (IR-MAD) algorithm may be used both for unsupervised change detection in multi- and hyperspectral remote sensing imagery and for automatic radiometric normalization of multitemporal image sequences. Principal components analysis (PCA), as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (nonlinear), may further enhance change signals relative to no-change background. IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric normalization, and kernel PCA/MAF/MNF transformations are presented that function as transparent and fully integrated extensions of the ENVI remote sensing image analysis environment. The train/test approach to kernel PCA is evaluated against a Hebbian learning procedure. Matlab code is also available that allows fast data exploration and experimentation with smaller datasets. New, multiresolution versions of IR-MAD that accelerate convergence and that further reduce no-change background noise are introduced. Computationally expensive matrix diagonalization and kernel image projections are programmed to run on massively parallel CUDA-enabled graphics processors, when available, giving an order of magnitude enhancement in computational speed. The software is available from the authors' Web sites.

Achieving higher uplink performance and capacity via non-overlapping window adaptive maximum noise fraction beamforming technique

This study introduces a practical use of maximum noise fraction (MNF) in beamforming antennas that enhances users' uplink performance and capacity in cellular systems. The study introduces a non-overlapping window adaptive MNF technique. In addition, it mathematically analyses the proposed method. Moreover, the performance benefits created via MNF technique in uplink scenarios is also studied. A multi-carrier wideband code division multiple access (MC-WCDMA) system is used as a toy example to represent the benefits created by the proposed technique when it is used as a beamformer. The performance of the proposed technique for uplink MC-WCDMA is mathematically analysed. Simulations are conducted to study the performance and the capacity of the proposed method. The effect of the noise covariance matrix estimation that is vital for the operation of MNF systems on the performance is investigated.

Comparison of feature extraction methods in dimensionality reduction

This technical note compares a number of feature extraction methods to determine which method enables higher accuracy of the performed classifications for dimensionality reduction in hyperspectral datasets. Two hyperspectral images were transformed into 10-, 15-, and 20-feature spaces using four unsupervised feature extraction methods (i.e., principal component analysis, maximum noise fraction, locally linear embedding (LLE), and independent component analysis) and one supervised feature extraction method (i.e., nonparametric weighted feature extraction, NWFE). A supervised classifier (i.e., support vector machine) processed a small number of training data and the feature spaces. The classification maps were compared with test samples, and then the classification accuracy of the feature extraction method was evaluated by kappa coefficient. With a 95% confidence interval of hypothesis testing, a 10-feature space could provide sufficient dimension for supervised classification and maximum noise fraction; and LLE outperformed the other feature extraction methods. Because NWFE might be limited by the small number of training samples, its classification performance was lower than those of the other feature extraction methods.

Kernel Maximum Autocorrelation Factor and Minimum Noise Fraction Transformations

This paper introduces kernel versions of maximum autocorrelation factor (MAF) analysis and minimum noise fraction (MNF) analysis. The kernel versions are based upon a dual formulation also termed Q-mode analysis in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version, the inner products of the original data are replaced by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution also known as the kernel trick these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component analysis (PCA), kernel MAF, and kernel MNF analyses handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function and then performing a linear analysis in that space. Three examples show the very successful application of kernel MAF/MNF analysis to: 1) change detection in DLR 3K camera data recorded 0.7 s apart over a busy motorway, 2) change detection in hyperspectral HyMap scanner data covering a small agricultural area, and 3) maize kernel inspection. In the cases shown, the kernel MAF/MNF transformation performs better than its linear counterpart as well as linear and kernel PCA. The leading kernel MAF/MNF variates seem to possess the ability to adapt to even abruptly varying multi and hypervariate backgrounds and focus on extreme observations.

Object-oriented subspace analysis for airborne hyperspectral remote sensing imagery

An object-oriented mapping approach based on subspace analysis of airborne hyperspectral images was investigated in this paper. Hyperspectral features were extracted based on subspace learning approaches, in order to reduce the redundancy of spectral space and extract the characteristic images for the further object-oriented classification. In this paper, three kinds of spectral feature extraction (FE) methods were utilized to obtain the subspace of airborne hyperspectral data: (1) unsupervised FE, such as PCA (principal component analysis), ICA (independent component analysis) and MNF (maximum noise fraction); (2) supervised FE, e.g. DBFE (decision boundary feature extraction), DAFE (discriminant analysis feature extraction) and NWFE (nonparametric weighted feature extraction); and (3) linear mixture analysis. Afterwards, the extracted subspace features were fed into the object-based classification system. The FNEA (fractal net evolution approach) was utilized to extract objects from the subspace images and SVM (support vector machines) was then used to classify the object-based features. Experiments were conducted on two airborne hyperspectral datasets: (1) the AVIRIS dataset over the northwest Indiana's Pine with 220 spectral bands (agricultural region), and (2) the ROSIS dataset over Pavia University, northern of Italy with 102 spectral bands (urban region). Results revealed that the proposed object-based approach could give significantly higher accuracies than the traditional pixel-based subspace classification.

A maximum noise fraction transform with improved noise estimation for hyperspectral images

Feature extraction is often performed to reduce spectral dimension of hyperspectral images before image classification. The maximum noise fraction (MNF) transform is one of the most commonly used spectral feature extraction methods. The spectral features in several bands of hyperspectral images are submerged by the noise. The MNF transform is advantageous over the principle component (PC) transform because it takes the noise information in the spatial domain into consideration. However, the experiments described in this paper demonstrate that classification accuracy is greatly influenced by the MNF transform when the ground objects are mixed together. The underlying mechanism of it is revealed and analyzed by mathematical theory. In order to improve the performance of classification after feature extraction when ground objects are mixed in hyperspectral images, a new MNF transform, with an improved method of estimating hyperspectral image noise covariance matrix (NCM), is presented. This improved MNF transform is applied to both the simulated data and real data. The results show that compared with the classical MNF transform, this new method enhanced the ability of feature extraction and increased classification accuracy.

An Adaptive Noise-Filtering Algorithm for AVIRIS Data With Implications for Classification Accuracy

This paper describes a new algorithm used to adaptively filter a remote-sensing data set based on signal-to-noise ratios (SNRs) once the maximum noise fraction has been applied. This algorithm uses Hermite splines to calculate the approximate area underneath the SNR curve as a function of band number, and that area is used to place bands into ldquobinsrdquo with other bands having similar SNRs. A median filter with a variable-sized kernel is then applied to each band, with the same size kernel used for each band in a particular bin. The proposed adaptive filters are applied to a hyperspectral image generated by the airborne visible/infrared imaging spectrometer sensor, and results are given for the identification of three different pine species located within the study area. The adaptive-filtering scheme improves image quality as shown by estimated SNRs. Classification accuracies of three pine species improved by more than 10% in the study area as compared to that achieved by the same discriminant method without adaptive spatial filtering.

As técnicas NASVD e MNF e sua aplicação na redução de ruídos em dados gamaespectrométricos

A desintegração radioativa é um processo aleatório e a estimativa de todas as medidas associadas é governada por leis estatísticas. Os perfis de taxas de contagem são sempre "ruidosos" quando utilizados períodos curtos como um segundo para cada medida. Os filtros utilizados e posteriormente as correções feitas no processamento atual de dados gamaespectrométricos não são suficientes para remover ou diminuir, consideravelmente, o ruído oriundo do espectro. Dois métodos estatísticos que atuam diretamente nos dados coletados, isto é, nos espectros, vêm sendo sugeridos na literatura para remover e minimizar estes ruídos remanescentes o Noise-Adjusted Singular Value Decomposition - NASVD e Maximum Noise Fraction - MNF. Estes métodos produzem uma redução no ruído de forma significativa. Neste trabalho eles foram implementados dentro do ambiente de processamento do software Oasis Montaj e aplicados na área compreendida pelos blocos I e II do levantamento aerogeofísico que recobre a porção oeste da Província Mineral do Tapajós, entre os Estados do Pará e Amazonas. Os dados filtrados e não-filtrados com as técnicas de NASVD e MNF foram processados com os parâmetros e constantes fornecidos pela empresa Lasa Engenharia e Prospecções S.A., sendo estes comparados. Os resultados da comparação entre perfis e mapas apresentaram-se de forma promissora, pois houve um ganho na resolução dos produtos.

Maximum noise fraction (MNF) transformation to remove ballistocardiographic artifacts in EEG signals recorded during fMRI scanning

Simultaneous electroencephalography (EEG) and magnetic resonance imaging (MRI) may allow imaging of the brain at high temporal and spatial resolution. However, EEGs recorded under these conditions are corrupted by large repetitive artifacts generated by the switching MR gradients and, second, by slightly less stable ballistocardiographic artifacts (BCG) resulting from heart beat related body movements. Here we present a new approach to remove BCG artifacts using a blind source separation (BSS) approach called maximum noise fraction (MNF). In contrast to other BSS methods MNF provides a set of components ordered by their signal-to noise-ratio. Applied to BCG contaminated EEG signals this means that components representing the artifact activity always result as the last or first ones (depending on the direction of ordering) thus making it easy to identify those components to be removed for artefact suppression. The new algorithm combines MNF and a subsequent template subtraction method to remove the BCG in a fully automatic manner. The efficiency of the new method was validated by comparing spontaneous EEG signals as well as event related potentials recorded from four subjects. According to these results MNF outperforms other BSS approaches in its capability to separate artifact activity from true EEG. In addition, MNF is superior to these alternatives regarding computational efficiency.

Spectral mixture analysis for mapping abundance of urban surface components from the Terra/ASTER data

Using a linear unconstrained least squares (LSS) method and a non-linear artificial neural network (ANN) algorithm, we conducted a spectral mixture analysis to the Advanced Spaceborne Thermal Emission and Reflectance Radiometer (ASTER) image data in Yokohama city, Japan, for mapping the abundance of the urban surface components. ASTER is a newly developed research facility instrument. The regions of interest of four endmembers (Vegetation, Soil, High/Low albedo impervious surfaces) were determined in Maximum Noise Fraction (MNF) feature spaces. The spectral signatures of the four endmembers were then extracted from the ASTER VNIR (15-m resolution) and SWIR (30-m resolution) imagery by referring to high spatial resolution airborne imagery (The Airborne Imaging Spectrometer, AISA, with 2-m resolution) and land use/land cover map for training and testing the LSS and ANN algorithms. Experimental results indicate that ASTER VNIR and SWIR image data are capable of mapping the abundances of urban surface components with a reasonable accuracy and that the ANN outperforms the unconstrained LSS in this spectral mixture analysis.

Mapping salt-marsh vegetation by multispectral and hyperspectral remote sensing

Tidal marshes are characterized by complex patterns both in their geomorphic and ecological features. Such patterns arise through the elaboration of a network structure driven by the tidal forcing and through the interaction between hydrodynamical, geophysical and ecological components (chiefly vegetation). Intertidal morphological and ecological structures possess characteristic extent (order of kilometers) and small-scale features (down to tens of centimeters) which are not simultaneously accessible through field observations, thus making remote sensing a necessary observation tool. This paper describes a set of remote sensing observations from several satellite and airborne platforms, the collection of concurrent ground reference data and the vegetation distributions that may be inferred from them, with specific application to the Lagoon of Venice (Italy). The data set comprises ROSIS, CASI, MIVIS, IKONOS and QuickBird acquisitions, which cover a wide range of spatial and spectral resolutions. We show that spatially-detailed and quantitatively reliable vegetation maps may be derived from remote sensing in tidal environments through unsupervised ( K-means) and supervised algorithms (Maximum Likelihood and Spectral Angle Mapper). We find that, for the objective of intertidal vegetation classification, hyperspectral data contain largely redundant information. This in particular implies that a reduction of the spectral features is required for the application of the Maximum Likelihood classifier. A large number of experiments with different feature extraction/selection algorithms show that the use of four bands derived from Maximum Noise Fraction transforms and four RGBI broad bands obtained by spectral averaging yield very similar classification performances. The classifications from hyperspectral data are somewhat superior to those from multispectral data, but the close performance and the results of the features reduction experiments show that spatial resolution affects classification accuracy much more importantly than spectral resolution. Monitoring schemes of tidal environment vegetation may thus be based on high-resolution satellite acquisitions accompanied by systematic ancillary field observations at a relatively limited number of reference sites, with practical consequences of some relevance.

Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis

In hyperspectral image analysis, the principal components analysis (PCA) and the maximum noise fraction (MNF) are most commonly used techniques for dimensionality reduction (DR), referred to as PCA-DR and MNF-DR, respectively. The criteria used by the PCA-DR and the MNF-DR are data variance and signal-to-noise ratio (SNR) which are designed to measure data second-order statistics. This paper presents an independent component analysis (ICA) approach to DR, to be called ICA-DR which uses mutual information as a criterion to measure data statistical independency that exceeds second-order statistics. As a result, the ICA-DR can capture information that cannot be retained or preserved by second-order statistics-based DR techniques. In order for the ICA-DR to perform effectively, the virtual dimensionality (VD) is introduced to estimate number of dimensions needed to be retained as opposed to the energy percentage that has been used by the PCA-DR and MNF-DR to determine energies contributed by signal sources and noise. Since there is no prioritization among components generated by the ICA-DR due to the use of random initial projection vectors, we further develop criteria and algorithms to measure the significance of information contained in each of ICA-generated components for component prioritization. Finally, a comparative study and analysis is conducted among the three DR techniques, PCA-DR, MNF-DR, and ICA-DR in two applications, endmember extraction and data compression where the proposed ICA-DR has been shown to provide advantages over the PCA-DR and MNF-DR.

Cleaning Scattered Multi-Channel Data

A new type of “maximum noise fraction” transform, for multivariate data, facilitates noise reduction without requiring the samples to vary continuously, and without need to collect “noise” statistics. The algorithm specifically targets data with a hundred or more channels. Its main applications will be to hyper-spectral remote sensing data and to airborne gamma-ray spectrometry.

Recent advances in aerial gamma-ray surveying

Aerial gamma-ray surveying uses NaI(Tl) detectors mounted in small aircraft to measure gamma radiation, emitted from the earth’s surface. The data are collected as gamma-ray spectra, typically with 1 s counting times, from which are derived K, U and Th concentrations in the ground. Applications of aerial surveying include geological mapping for mineral exploration, soil mapping for agriculture, pollution studies and location of lost sources. Recent advances in applying statistical methods to the spectral data have resulted in large reductions in the noise levels in the surveys. Some of the methods available to do this include noise adjusted singular value decomposition (NASVD) [Proceedings of Exploration 97: Fourth Decennial International Conference on Mineral Exploration (1997) 753] and maximum noise fraction (MNF) and enhanced MNF (eMNF) [Explor. Geophys. 31 (2000) 73]. These methods, in general, apply normalization for variance to the spectra, use a principal component method to obtain the “significant” components of the data and reconstruct cleaned spectra, which are then processed in a standard manner to get radionuclide concentrations. However, they differ in the detail of the application and thus give slightly different results. In this paper, the application of noise reduction methods to various synthetic surveys is used to examine the strengths and weaknesses of the methods. In tests where there are high correlations between U and Th, the eMNF method performs best although the results are improved by prior clustering of the data by the Th/U ratio. If the data show no correlations, then the effectiveness of all the noise removal methods is reduced. If a data set is small (<1500 spectra), then MNF appears to be the better method. Consideration of the various tests suggests an optimum process whereby spectra are sorted into groups by the Th/U ratio of areas identified in a standard processing and then cleaned by eMNF or MNF, depending on the number of spectra in each group.

Reducing noise in gamma-ray spectrometry using spectral component analysis

Statistical methods for removing noise from multichannel spectra are now routinely applied in gamma-ray spectrometry. The two methods in common use are the Noise Adjusted Singular Value Decomposition (NASVD) method and the Maximum Noise Fraction (MNF) method. These methods use a principal component (PC) type analysis to extract the dominant spectral shapes from a dataset. These PCs are used to reconstruct spectra that have most of the original signal, but little of the noise. The NASVD and MNF methods differ mainly in how they normalise the input spectra for noise before spectral component analysis. The purpose of this paper is to evaluate these methods in terms of both the accuracy and precision of the resultant noise-reduced spectra.We develop a methodology based on the use of a synthetic spectra dataset where the true spectrum channel count rates (in the absence of noise) are known. Because the true values are known, by repeatedly processing the same synthetic data using different synthesised noise we derive estimates of both the precision and accuracy of the processed data.Our tests using synthetic data show that the NASVD and MNF methods produce almost identical results. This suggests that the differences in the way the methods normalise for noise are not of great significance. However, the MNF method produces results that are fractionally better in terms of both precision and accuracy. This may be a function of the robustness of the numerical algorithms we used to implement these methods.

Spectral methods for reducing noise in gamma-ray spectrometry

Statistical methods for removing noise from multichannel spectra are now routinely applied in gamma-ray spectrometry. The two methods in common use are the Maximum Noise Fraction (MNF) method and the Noise Adjusted Singular Value Decomposition (NASVD) method. These methods use a principal component (PC) type analysis to extract the dominant spectral shapes from a dataset. These PCs are then used to construct smooth spectra. The purpose of this paper is to evaluate current spectral smoothing methods in terms of both their accuracy and precision.We develop a methodology based on the use of a synthetic spectra dataset where the true spectrum channel count rates (in the absence of noise) are known. By repeatedly processing the same synthetic data using different synthesised noise, and because the true values of the synthetic data are known, we derive estimates of both the precision and accuracy of the processed data.Our tests using synthetic data show that the MNF and NASVD methods produce almost identical results. However, the MNF method produces results that are fractionally better in terms of both precision and accuracy. This may be a function of the robustness of the numerical algorithms we used to implement these methods.

Discussion on: "Noise Reduction of Aerial Gamma-Ray Surveys"

Dickson and Taylor (1998) evaluated the NASVD (Noise Adjusted Singular Value Decomposition, Hovgaard, 1997) and MNF (Maximum Noise Fraction, Green et al., 1988; Lee et al., 1990) methods for reducing noise in gamma-ray spectra. They showed (Table 1) that the MNF method is far more effective at reducing noise than the NASVD method. This result is surprising, since my own experience and that of other researchers in this field (Hovgaard, personal communication) is that the two methods give similar results.