Effective denoising and classification of hyperspectral images using curvelet transform and singular spectrum analysis

Hyperspectral imaging (HSI) classification has become a popular research topic in recent years, and effective feature extraction is an important step before the classification task. Traditionally, spectral feature extraction techniques are applied to the HSI data cube directly. This paper presents a novel algorithm for HSI feature extraction by exploiting the curvelet transformed domain via a relatively new spectral feature processing technique – singular spectrum analysis (SSA). Although the wavelet transform has been widely applied for HSI data analysis, the curvelet transform is employed in this paper since it is able to separate image geometric details and background noise effectively. Using the support vector machine (SVM) classifier, experimental results have shown that features extracted by SSA on curvelet coefficients have better performance in terms of classification accuracies over features extracted on wavelet coefficients. Since the proposed approach mainly relies on SSA for feature extraction on the spectral dimension, it actually belongs to the spectral feature extraction category. Therefore, the proposed method has also been compared with some state-of-the-art spectral feature extraction techniques to show its efficacy. In addition, it has been proven that the proposed method is able to remove the undesirable artefacts introduced during the data acquisition process as well. By adding an extra spatial post-processing step to the classified map achieved using the proposed approach, we have shown that the classification performance is comparable with several recent spectral-spatial classification methods

SCSA based MATLAB pre-processing toolbox for 1H MR spectroscopic water suppression and denoising

In vivo 1H Magnetic Resonance Spectroscopy (MRS) is a useful tool in assessing neurological and metabolic disease, and to improve tumor treatment. Different pre-processing pipelines have been developed to obtain optimal results from the acquired data with sophisticated data fitting, peak suppression, and denoising protocols. We introduce a Semi-Classical Signal Analysis (SCSA) based Spectroscopy pre-processing toolbox for water suppression and data denoising, which allows researchers to perform water suppression using SCSA with phase correction and apodization filters and denoising of MRS data, and data fitting has been included as an additional feature, but it is not the main aim of the work. The fitting module can be passed on to other software. The toolbox is easy to install and to use: 1) import water unsuppressed MRS data acquired in Siemens, Philips and .mat file format and allow visualization of spectroscopy data, 2) allow pre-processing of single voxel and multi-voxel spectra, 3) perform water suppression and denoising using SCSA, 4) incorporate iterative nonlinear least squares fitting as an extra feature. This article provides information about how the above features have been included, along with details of the graphical user interface using these features in MATLAB

Spectral Representations of One-Homogeneous Functionals

This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further useful properties related to orthogonality of the decomposition and the Parseval identity. The spectral transform is motivated by total variation and further developed to higher order variants. Moreover, we show that the approach can recover Fourier analysis as a special case using an appropriate $\ell^1$-type functional and discuss a coupled sparsity example

Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)

Application of signal processing methods to the Rover Environmental Monitoring Station data for the analysis of environmental processes on Mars

La presente tesis analiza los datos de dos de los sensores de la estación meteorológica REMS, localizada Mars Science Laboratory (MSL), activa en Marte desde agosto de 2012: el sensor de presión (PS) y los sensores de temperatura del aire (ATS). La información contenida en los datos de estos sensores es muy valiosa y reveladora para comprender mejor los procesos meteorológicos que tienen lugar diariamente en Marte. Es necesario conocer en profundidad el funcionamiento de ambos sensores y el flujo de procesamiento de datos que se sigue para transformar los datos digitales recibidos de Marte en información tangible y legible. El objetivo principal de esta tesis es utilizar métodos de procesado de señal que nos ayuden a extraer información útil contenida en los datos de estos sensores, que no son visible a simple vista. Se desea extraer información relacionada con procesos ambientales de Marte, contribuyendo así a una mejor comprensión del planeta rojo. Con todos estos conocimientos adquiridos, se ha realizado una investigación exhaustiva de los métodos de procesamiento de señales para encontrar los mejores que se ajusten a nuestros datos y nos ayuden a encontrar la información relacionada con procesos ambientales. Usando los datos del PS y del ATS, han utilizado wavelets para quitar ruido en los datos del ATS y el algoritmo de Análisis de Espectro Singular (SSA) para encontrar indicadores relacionados con los procesos ambientales en Marte. Se han encontrado precursores de tormentas de polvo en los datos del PS y posibles nubes de hielo en los datos ATS, ambos utilizando el algoritmo SSA

An Automatic Tool for Partial Discharge De-noising via Short Time Fourier Transform and Matrix Factorization

This paper develops a fully automatic tool for the denoising of partial discharge (PD) signals occurring in electrical power networks and recorded in on-site measurements. The proposed method is based on the spectral decomposition of the PD measured signal via the joint application of the short-time Fourier transform and the singular value decomposition. The estimated noiseless signal is reconstructed via a clever selection of the dominant contributions, which allows us to filter out the different spurious components, including the white noise and the discrete spectrum noise. The method offers a viable solution which can be easily integrated within the measurement apparatus, with unavoidable beneficial effects in the detection of important parameters of the signal for PD localization. The performance of the proposed tool is first demonstrated on a synthetic test signal and then it is applied to real measured data. A cross comparison of the proposed method and other state-of-the-art alternatives is included in the study