Assessment of noise reduction of hyperspectral imagery using a target detection application

This article presents an evaluation of a previously proposed noise reduction technique for hyperspectral imagery with regard to its use in remote sensing applications. Target detection from hyperspectral imagery was selected as an example for the evaluation. A hyperspectral datacube acquired using the airborne Shortwave Infrared Full Spectrum Imager (SFSI)-II with man-made targets deployed in the scene of the datacube was tested. In addition to an evaluation using the receiver operating characteristic (ROC) curve approach, we used a spectral unmixing technique to generate the fraction images of the target materials, measured the area of the targets derived from the datacube before and after applying the noise reduction technology, and then compared the derived target areas to the real targets to assess the detectability of the targets. The area ratio between a derived target and the real target was used as the criterion in the evaluation. The evaluation results show that the noise reduction technique can help to better serve remote sensing applications. The small targets that cannot be detected from the original datacube were detected after the noise reduction using the technology.     

Exploiting the Toeplitz structure in certain queueing problems

Toeplitz matrices model a wide variety of problems in queueing theory, however, the advanced algorithmic tools developed in the field of Toeplitz computations are not generally used in the solution of queueing problems. In this paper we make a survey of some very recent results where concepts as displacement rank, Schur complement, FFT and fast polynomial computations, encountered in Toeplitz matrix analysis, are exploited in order to devise very efficient algorithms for solving a wide class of queueing problems.     

Estimating forest stand structure from high resolution imagery using the directional variogram

The height and stocking of forest stands can be estimated with relatively high precision using an empirical model relating parameters extracted from the directional variogram of high resolution images and forest structure parameters. A geometrical-optical model of the forest was first used to generate images of artificial forest stands in order to establish the relation between tree size. tree density and image texture. The resulting equations were then applied on the computer generated images as well as on high resolution MEIS II images to predict the forest structure values. The results show a good concordance between actual and predicted values, even when spatial resolution was degraded from 0·36m to 2·16m.     

Progressive dimensionality reduction by transform for hyperspectral imagery

This paper develops to a new concept, called progressive dimensionality reduction by transform (PDRT), which is particularly designed to perform data dimensionality reduction in terms of progressive information preservation. In order to materialize the PRDT a key issue is to prioritize information contained in each spectral-transformed component so that all the spectral transformed components will be ranked in accordance with their information priorities. In doing so, projection pursuit (PP)-based dimensionality reduction by transform (DRT) techniques are developed for this purpose where the Projection Index (PI) is used to define the direction of interestingness of a PP-transformed component, referred to as projection index component (PIC). The information contained in a PIC is then calculated by the PI and used as the priority score of this particular PIC. Such a resultant PDRT is called progressive dimensionality reduction by projection index-based projection pursuit (PDR-PIPP) which performs PDRT by retaining an appropriate set of PICs for information preservation according to their priorities. Two procedures are further developed to carry out PDR-PIPP in a forward or a backward manner, referred to forward PDR-PIPP (FPDR-PIPP) or backward PDRT (BPDR-PIPP), respectively, where FPDR-PIPP can be considered as progressive band expansion by starting with a minimum number of PICs and adding new PICs progressively according to their reduced priorities as opposed to BPDRT which can be regarded progressive band reduction by beginning with a maximum number of PICs and removing PICs with least priorities progressively. Both procedures are terminated when a stopping rule is satisfied. The advantages of PDR-PIPP allow users to transmit, communicate, process and store data more efficiently and effectively in the sense of retaining data integrity progressively.     

Multivariate forest structure modelling and mapping using high resolution airborne imagery and topographic information

Remote sensing has been widely used for modelling and mapping individual forest structural attributes, such as LAI and stem density, however the development and evaluation of methods for simultaneously modelling and mapping multivariate aspects of forest structure are comparatively limited. Multivariate representation of forest structure can be used as a means to infer other environmental attributes such as biodiversity and habitat, which have often been shown to be enhanced in more structurally diverse or complex forests. Image-based modelling of multivariate forest structure is useful in developing an understanding of the associations between different aspects of vertical and horizontal structure and image characteristics. Models can also be applied spatially to all image pixels to produce maps of multivariate forest structure as an alternative to sample-based field assessment. This research used high spatial resolution multispectral airborne imagery to provide spectral, spatial, and object-based information in the development of a model of multivariate forest structure as represented by twenty-four field variables measured in plots within a temperate hardwood forest in southern Quebec, Canada. Redundancy Analysis (RDA) was used to develop a model that explained a statistically significant proportion of the variance of these structural attributes. The resulting model included image variables representing mostly within-crown and within-shadow brightness variance (texture) as well as elevation, taken from a DEM of the study area. It was applied spatially across the entire study area to produce a continuous map of predicted multivariate forest structure. Bootstrapping validation of the model provided an RMSE of 19.9%, while independent field validation of mapped areas of complex and simple structure showed accuracies of 89% and 69%, respectively. Multiscale testing using resampled imagery suggested that the methods could possibly be used with current pan-sharpened, or future sub-metre resolution, multispectral satellite imagery, which would provide much greater spatial coverage and reduced image processing compared to airborne imagery.     

Fast robust regression algorithms for problems with Toeplitz structure

The problem of computing an approximate solution of an overdetermined system of linear equations is considered. The usual approach to the problem is least squares, in which the 2-norm of the residual is minimized. This produces the minimum variance unbiased estimator of the solution when the errors in the observations are independent and normally distributed with mean 0 and constant variance. It is well known, however, that the least squares solution is not robust if outliers occur, i.e., if some of the observations are contaminated by large error. In this case, alternate approaches have been proposed which judge the size of the residual in a way that is less sensitive to these components. These include the Huber M-function, the Talwar function, the logistic function, the Fair function, and the ?₁ norm. New algorithms are proposed to compute the solution to these problems efficiently, in particular, when the matrix A has small displacement rank. Matrices with small displacement rank include matrices that are Toeplitz, block-Toeplitz, block-Toeplitz with Toeplitz blocks, Toeplitz plus Hankel, and a variety of other forms. For exposition, only Toeplitz matrices are considered, but the ideas apply to all matrices with small displacement rank. Algorithms are also presented to compute the solution efficiently when a regularization term is included to handle the case when the matrix of the coefficients is ill-conditioned or rank-deficient. The techniques are illustrated on a problem of FIR system identification.     

Exploring dimensionality reduction of EEG features in motor imagery task classification

A Brain-Computer Interface (BCI) system based on motor imagery (MI) identifies patterns of electrical brain activity to predict the user intention while certain movement imagination tasks are performed. Currently, one of the most important challenges is the adaptive design of a BCI system. For solving it, this work explores dimensionality reduction techniques: once features have been extracted from Electroencephalogram (EEG) signals, the high-dimensional EEG data has to be mapped onto a new reduced feature space to make easier the classification stage. Besides the standard sequential feature selection methods, this paper analyzes two unsupervised transformation-based approaches – Principal Component Analysis and Locality Preserving Projections – and the Local Fisher Discriminant Analysis (LFDA), which works in a supervised manner. The dimensionality in the projected space is chosen following a wrapper-based approach by an efficient leave-one-out estimation. Experiments have been conducted on five novice subjects during their first sessions with MI-based BCI systems in order to show that the appropriate use of dimensionality reduction methods allows increasing the performance. In particular, obtained results show that LFDA gives a significant enhancement in classification terms without increasing the computational complexity and, then, it is a promising technique for designing MI-based BCI system.     

Denoising and dimensionality reduction of hyperspectral imagery using wavelet packets,neighbour shrinking and principal component analysis

After dimensionality reduction of a hyperspectral datacube using principal component analysis (PCA), the dimension-reduced channels often contain a significant amount of noise. To overcome this problem, this letter proposes a method that can fulfil both denoising and dimensionality reduction of hyperspectral data using wavelet packets, neighbour wavelet shrinking and PCA. A 2D forward wavelet packet transform is performed in the spatial domain on each of the band images of a hyperspectral datacube, the wavelet packet coefficients are then shrunk by employing a neighbourhood wavelet thresholding scheme, and an inverse 2D wavelet packet transform is performed on the thresholded coefficients to create the denoised datacube. PCA is applied on the denoised datacube in the spectral domain to obtain the dimension-reduced datacube. Experiments conducted in this letter confirm the feasibility of the proposed method for denoising and dimensionality reduction of hyperspectral data.     

Change detection using landsat photographic imagery

If a negative and a positive transparency of the same image at the same scale are overlaid, then the result will be a completely uniform neutral-colored composite with no information content. When the images are temporally separated, those areas which have changed are highlighted, and the unchanged areas appear as a neutral background. Multichannel-temporal change can be determined by using three-color composite transparencies. Positive and negative transparencies of Landsat images at a scale of approximately 1:1,000,000 can be purchased quite inexpensively, making this technique of flagging change very economical.     

Mapping nonnative plants using hyperspectral imagery

Nonnative plant species are causing enormous ecological and environmental impacts from local to global scale. Remote sensing images have had mixed success in providing spatial information on land cover characteristics to land managers that increase effective management of invasions into native habitats. However, there has been limited evaluation of the use of hyperspectral data and processing techniques for mapping specific invasive species based on their spectral characteristics. This research evaluated three different methods of processing hyperspectral imagery: minimum noise fraction (MNF), continuum removal, and band ratio indices for mapping iceplant (Carpobrotus edulis) and jubata grass (Cortaderia jubata) in California's coastal habitat. Validation with field sampling data showed high mapping accuracies for all methods for identifying presence or absence of iceplant (97%), with the MNF procedure producing the highest accuracy (55%) when the classes were divided into four different densities of iceplant.     

Crop discrimination using multi-temporal SAR imagery

Seven ERS-1 SAR images obtained at different dates during the 1993 crop growing season are used in a study of the potential of multi-temporal SAR for agricultural crop discrimination for an area near Feltwell, Norfolk, UK. The study compares a per-pixel and a per-field approach. Pixel-based classification is based on raw intensity images, temporal subtraction images, filtered images, and texture features. Field-based classification uses the mean back-scatter coefficient derived for each field. Analysis of the contribution of each dataset uses statistical separability measures and confusion matrix methods. The classification algorithms used are maximum likelihood and Kohonen's self-organized feature map (SOM). We find that SAR-based texture features contribute nothing to crop discrimination. Filtered images produce the best result for the per-pixel approach, giving a classification accuracy of around 60%. The use of a SOM for field-based classification produces a classification accuracy greater than 75%. This is not a surprising result, as field-based classifications use averaged data, in which the noise effect is reduced.     

New preconditioners for systems of linear equations with Toeplitz structure

In this paper, we consider applying the preconditioned conjugate gradient (PCG) method to solve system of linear equations $T x = \mathbf b $ where $T$ is a block Toeplitz matrix with Toeplitz blocks (BTTB). We first consider Level-2 circulant preconditioners based on generalized Jackson kernels. Then, BTTB preconditioners based on a splitting of BTTB matrices are proposed. We show that the BTTB preconditioners based on splitting are special cases of embedding-based BTTB preconditioners, which are also good BTTB preconditioners. As an application, we apply the proposed preconditioners to solve BTTB least squares problems. Our preconditioners work for BTTB systems with nonnegative generating functions. The implementations of the construction of the preconditioners and the relevant matrix-vector multiplications are also presented. Finally, Numerical examples, including image restoration problems, are presented to demonstrate the efficiency of our proposed preconditioners.     

Speckle reduction in polarimetric SAR imagery with stochastic distances and nonlocal means

This paper presents a technique for reducing speckle in Polarimetric Synthetic Aperture Radar (PolSAR) imagery using nonlocal means and a statistical test based on stochastic divergences. The main objective is to select homogeneous pixels in the filtering area through statistical tests between distributions. This proposal uses the complex Wishart model to describe PolSAR data, but the technique can be extended to other models. The weights of the location-variant linear filter are function of the p-values of tests which verify the hypothesis that two samples come from the same distribution and, therefore, can be used to compute a local mean. The test stems from the family of (h  –?$?$) divergences which originated in Information Theory. This novel technique was compared with the Boxcar, Refined Lee and IDAN filters. Image quality assessment methods on simulated and real data are employed to validate the performance of this approach. We show that the proposed filter also enhances the polarimetric entropy and preserves the scattering information of the targets.     

A two-step nearest neighbors algorithm using satellite imagery for predicting forest structure within species composition classes

Nearest neighbors techniques have been shown to be useful for predicting multiple forest attributes from forest inventory and Landsat satellite image data. However, in regions lacking good digital land cover information, nearest neighbors selected to predict continuous variables such as tree volume must be selected without regard to relevant categorical variables such as forest/non-forest. The result is that non-zero volume predictions may be obtained for pixels predicted to be non-forest, and volume predictions for pixels predicted to be forest may be erroneously small due to non-forest nearest neighbors. For users who wish to circumvent this discrepancy, a two-step algorithm is proposed in which the class of a relevant categorical variable such as land cover is predicted in the first step, and continuous variables such as volume are predicted in the second step subject to the constraint that all nearest neighbors must come from the predicted class of the categorical variable. Nearest neighbors, multinomial logistic regression, and discriminant analysis techniques were investigated for use in the first step. The results were generally similar for the three techniques, although the multinomial logistic regression technique was slightly superior. The k-Nearest Neighbors technique was used in the second step because many continuous forest inventory variables do not satisfy the distributional assumptions necessary for parametric multivariate techniques. The results for six 15-km × 15-km areas of interest in northern Minnesota, USA, indicate that areal estimates of tree volume, basal area, and density obtained from pixel predictions are comparable to plot-based estimates and estimates by conifer and deciduous classes are also comparable to plot-based estimates. When a mixed conifer/deciduous class was included, predictions for the mixed and deciduous class were confused.     

Mapping of coastal-water turbidity using LANDSAT imagery

Secchi disk depth was recorded in the field all along the Swedish coastline and compared with LANDSAT data. Chromaticity analysis was applied in the evaluation to allow for Sun angle and atmospheric corrections. The data were used to study the relative nutrient and solids loading situations around the Swedish coast and as a basis for the applicability of laser bathymetry for water depth soundings     

Characterizing land cover dynamics using multi-temporal imagery

An analysis of land cover changes was performed using a time-series of five SPOT HRV images for an area of the State of Rond°onia (western Brazilian Amazon) from 1986 to 1992. The total deforested area and the fraction of land abandoned to secondary vegetation were determined by means of image classification and Geographical Information System (GIS) techniques. Areas deforested by 1986 were traced throughout the period to estimate the fraction of land remaining continuously in the secondary vegetation category, possibly forming older secondary vegetation.     

An improved neural network technique for data dimensionality reduction in remotely sensed imagery

An approach for non-linear projection of multidimensional data is discussed with application to remotely sensed imagery. The approach uses a multi-layer neural network in auto-associative mode with an improved updating rule, based on a conjugate gradient. To evaluate the usefulness of the proposed approach, we used the maximum likelihood classifier applied to a Landsat TM image of Kénitra region (Morocco).