Accurate estimation of the noise present in hyperspectral images is crucial for the application of various processing algorithms. Works on noise statistics in hyperspectral data have focused on the estimation of noise variances in the spectral bands. These methods implicitly assume that all spatial pixels have the same noise distributions. However, this is not true for pushbroom sensors, which have two-dimensional detector arrays where the electro-optical characteristics of a detector vary from its neighbors in either dimension. We present a method to estimate the noise variances in all the individual detectors. The modified residual method provides a structure for analyzing the noise statistics in hyperspectral images but assumes uniform noise statistics across all spatial pixels. Starting with that methodology, we develop a method to estimate the noise statistics in individual spatial as well as spectral detector pixels, even when the noise is signal dependent. Results on simulated data show that the proposed method estimates the individual noise variances more accurately than both the classic methods and state-of-the-art deep learning methods. The application of the method to noise removal indicates a visible improvement in noisy data. (c) 2025 Society of Photo-Optical Instrumentation Engineers (SPIE)

Modeling of the underlying noise in a hyperspectral image reveals important information about the characteristics of the hyperspectral sensor and the image itself. While the focus in the literature has mostly been on the estimation of noise statistics, it is also of interest to estimate the actual noise present in each pixel, which can not only directly contribute to denoising of the image but can also aid other image processing algorithms exploiting such information. In this letter, we propose a novel method for per-pixel noise estimation that is also able to deal with spectral correlation in the noise. The method makes no assumptions on the behavior of the underlying noise. Simulation results show that the proposed method performs significantly better than the existing methods in cases where there is a correlation in the noise.

Accurate estimation of the underlying noise statistics is vital for the good performance of many hyperspectral image processing algorithms.Our proposed method can be used to estimate the full covariance matrix of the noise in the case where spectral correlation is present in the noise. However, this did not cater for the case of signal-dependent noise. In this paper, we extend the framework already proposedto the case of signal-dependent noise and propose a method to estimate the parameters of the signal-dependent noise variance even if the noise is spectrally correlated. It is shown that the proposed method can accurately estimate the different noise parameters in artificial datasets and even in the uncorrelated case usually gives better performance than the existing methods. Finally, the method is also applied and analysed in real datasets.

Echocardiogram metadata annotation is an entry level to the interpretation and analysis of echocardiographs for clinical usage. Automation of this task has been the subject of research over the past few years. In this paper we evaluate how far some state-of-the-art convolutional neural networks (CNNs) trained with non-radiological images can go at extracting features from cardiac structures in apical two-chamber (2CH) and four-chamber (4CH) echocardiograms for automatic binary view echocardiogram classification on a publicly available ultrasound dataset.

Accurate estimation of the underlying noise is vital in the processing of hyperspectral images (HSIs). Previous studies have shown that many HSI processing algorithms perform poorly if the noise is not correctly estimated. The classic residual (CR) method is commonly employed for the estimation of variance of the noise in different spectral bands. However, noise estimates as per the CR method ignore the presence of spectral or spatial correlation amongst noise samples. Some studies have been conducted in the past to investigate the spectral and spatial correlation present in the noise but there are very few methods available to estimate the correlations present in the noise. In this paper, we present a reliable method for the estimation of the spectral correlation in the noise. Recently, it was shown that the CR method performs poorly when estimating the spectral correlation in the noise. By using both artificial and real datasets, we show that the proposed new method estimates the noise spectral correlation significantly more accurately than the CR method.

Many Hyperspectral image (HSI) processing algorithms require an accurate estimate of the underlying noise for them to perform correctly. In many cases, only an estimate of the noise statistics is required. Many papers have tried to tackle this problem of HSI noise statistics estimation in the past. One of the well known methods of noise estimation is to exploit the inherent redundancy in the HSI by employing multiple regression [1-3] and using the residuals to approximate the noise. In this paper, we have improved upon the classic multiple regression based noise statistics estimator [2, 3]. This is achieved by modeling the regression procedure in a slightly different manner and making some useful approximations. Simulation results demonstrate an improvement over the classic residual-based noise estimates. The method is also applied to a real dataset.

Many hyperspectral image processing algorithms (e.g., detection, classification, endmember extraction, and so on) are generally designed with the assumption of no spectral or spatial correlation in noise. However, previous studies have shown the presence of nonnegligible correlation between the noise samples in different spectral bands, especially between noises in adjacent bands, and that most of the well-known intrinsic dimension estimation algorithms give poor estimates in the presence of correlated noise. Thus, there is a need to tackle the specific case of spectrally correlated noise for noise estimation. We show, in this paper, that the commonly employed hyperspectral noise estimation algorithm based on regression residuals can be significantly affected by spectrally correlated noise and we suggest a modified approach that proves to be robust to noise correlation. Furthermore, the proposed method improves the noise variance estimates in comparison to the classic residual method even for the case of uncorrelated noise. Simulation results show that the estimation error is reduced at times by a factor of 5 when there is high spectral correlation in the noise. Our proposed per-pixel noise estimator requires an estimate of the noise covariance matrix, and for this, we also propose a method to estimate the noise covariance matrix. Simulation results demonstrate that the per-pixel noise estimates obtained via the use of estimated noise statistics are almost as good as those obtained via use of the true statistics.

Hyperspectral images (HSI) have found widespread application in many disciplines because of their ability to characterize the object being imaged in a much more detailed manner as compared to colored or multispectral images. An accurate modelling of the underlying noise is, however, necessary in order to extract the useful data from the HSI. Although, classically noise in HSI has been modelled as independent of the signal, and spatially and spectrally uncorrelated, recent studies have shown the signal dependence of the noise as well as the presence of spectral correlation in the noise. In this work, we focus on the spectral correlation characteristic of noise in hyperspectral images. We make use of the multiple regression/residual method and provide an accurate analytical model for representation of noise variances and noise spectral covariances in terms of the residuals. We test the suitability of the classic residual model as well as our proposed analytical model for both artificially created and real datasets and show that the classic residual method does not provide an accurate model for the estimation of the noise covariance matrix.

The intrinsic dimension (ID) of a hyperspectral image (HSI) is an important prior knowledge for unsupervised unmixing. Incorrect determination of this number may have adverse effects on the unmixing results. Several methods have been developed to determine the ID, including Harsanyi-Farrand-Chang (HFC), Hysime, and random matrix theory (RMT). Previous work has shown that real HSI images could contain a certain amount of spectrally correlated noise, and noise approximation as well as ID estimation would suffer from it. This paper compares the performance of ID estimation methods with respect to various noise approximation methods, types of data, and parameters such as noise levels and correlation, noise approximation methods, and number of endmembers. It shows that a significant improvement can be obtained with most ID estimation methods by adapting them to the case where spectral correlation in the noise is considered as well.

of the Witwatersrand from 1969 to 1979.He spent his career in teaching and doing research in computational and mathematical modelling.The unifying theme of the symposium was computational and mathematical modelling in the broadest sense.Starfield's 60th anniversary was celebrated by a symposium for which the presentations were made by his colleagues of long standing.The proceedings of that symposium were published in the South African Journal of Science as the Starfield Festschrift. 1 The symposium on Starfield's 70th anniversary looked to the future of mathematical and computational modelling in the 21st century, with an emphasis on the contributions of a new generation of modellers.Starfield's keynote paper -'Ubiquitous modelling' -opened the symposium.He reviewed the development of modelling over the past 50 years; the ideas expressed in his paper were well illustrated by the symposium itself.

Seafloor massive sulphides are deep sea mineral deposits currently being examined as a potential mining resource. Conventional sonar bathymetry products gathered by sea surface platforms do not achieve adequate spatial resolution to detect these resources. High-resolution beamforming methods (such as multiple signal classification and estimation of signal parameters via rotational invariance techniques) improve the resolution of sonar bathymetry. We perform a quantitative review of these high-resolution methods using a novel simulator, showing results in the absence of platform motion for a single ping cycle. It was found that high-resolution methods achieved greater bathymetric accuracy and higher resolution than conventional beamforming and that these methods may be adequate for this style of marine exploration. These methods were also robust in the presence of unwanted persistent signals and low signal to noise ratios.

Many hyperspectral image processing algorithms (e.g detection, classification, endmember extraction etc.) are generally designed with the assumption of no spectral or spatial correlation in noise. However, studies [1, 2] have shown the presence of non-negligible correlation between the noise samples in different spectral bands, especially between noise of adjacent bands. It was also shown recently [3] that many well-known endmember extraction algorithms e.g. [4] give poor estimates for the number of endmembers in the presence of correlated noise. This asks for a precise estimation of noise for cases where noise is spectrally correlated. We show in this paper that the commonly employed hyperspectral noise estimation algorithm based on regression residuals [5, 6, 4] is very affected by spectrally correlated noise and we suggest a modified approach that proves to be very robust to noise correlation. Simulation results show that the estimation error is reduced at times by a factor of 5 when there is high spectral correlation in the noise.

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process and under- or over-estimation of this number may lead to incorrect unmixing for unsupervised methods. Most methods for estimating the intrinsic dimension require an estimate of the noise in the image, and noise estimates are often inaccurate in the presence of spectrally correlated noise. Since hyperspectral images are known to contain such correlated noise, intrinsic dimension estimations may be overestimated. In this paper we discuss the effect of correlation, as well as possible methods for overcoming such limitations. For instance, correlated bands may be removed prior to noise estimation, or spatially-based noise approximation methods may be used in place of statistical methods. These suggestions are implemented on synthetic and real images, including images acquired by AVIRIS, Hyperion and SpecTIR.

Studies on real hyperspectral data have shown that spectrally correlated noise may have a negative impact on noise approximation methods and hence on procedures that require accurate noise estimates, for example intrinsic dimension estimation. The exact behavior of this noise and the best method to overcome its effect is not well understood. In this paper we study this effect in a synthetic dataset by creating an image with areas of spatial homogeneity based on the geography of a Cuprite scene. Cosines with varying frequencies are used as endmembers, and various types of noise are added in order to analyze the effect. We found that we were able to create partial correlation coefficients which were similar to those found in real images. Also, correlated and uncorrelated noise were separable, and removal of correlated bands resulted in partial correlation coefficients consistent with images containing no correlated noise. These findings mean that it is possible to threshold to remove bands containing highly correlated noise for the improvement of noise estimation or of intrinsic dimension algorithms.

Hyperspectral imaging and subsequent analysis of drill cores is becoming a valuable tool in the mining and mineral exploration industries. Data can be rapidly obtained and spectral analysis avoids subjectivity in mineral identification. However, the core is presented in multiple core trays and separating it from the rock material has proved problematic unless the trays are perfectly aligned.This paper presents a new image processing method for handling this problem. It is robust and insensitive to rotation and contamination of the tray material by dust.

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process and under- or overestimation of this number may lead to incorrect unmixing in unsupervised methods. In this paper, we discuss a new method for determining the intrinsic dimension using recent advances in random matrix theory. This method is entirely unsupervised, free from any user-determined parameters and allows spectrally correlated noise in the data. Robustness tests are run on synthetic data, to determine how the results were affected by noise levels, noise variability, noise approximation, and spectral characteristics of the endmembers. Success rates are determined for many different synthetic images, and the method is tested on two pairs of real images, namely a Cuprite scene taken from Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) and SpecTIR sensors, and a Lunar Lakes scene taken from AVIRIS and Hyperion, with good results.

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process, and under- or over-estimation of this number may lead to incorrect unmixing for unsupervised methods. It is known that most real images contain noise that is not i.i.d. across bands, and so methods that assume i.i.d. noise are often avoided. However, this problem may be alleviated by implementing a noise whitening procedure as a pre-processing step. In this paper we will investigate one particular noise whitening approach, as well as a noise removal approach, and consider how the application of these methods may improve several methods for determining the intrinsic dimension of an image, including Malinowski's Empirical Indicator Function [1], Random Matrix Theory [2], and Harsanyi-Farrand-Chang [3].

It is very difficult to analyse large amounts of hyperspectral data. Here we present a method based on reducing the dimensionality of the data and clustering the result in moving toward classification of the data. Dimensionality reduction is done with diffusion maps, which interpret the eigenfunctions of Markov matrices as a system of coordinates on the original dataset in order to obtain an efficient representation of data geometric descriptions. Clustering is done using k-means and a neural network clustering theory, Fuzzy ART (FA). The process is done on a subset of core data from AngloGold Ashanti, and compared to results obtained by AngloGold Ashanti's proprietary method. Experimental results show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals in core samples.