Blind decomposition of transmission light microscopic hyperspectral cube using sparse representation

Abstract-In this paper, we address the problem of fully automated decomposition of hyperspectral images for transmission light microscopy. The hyperspectral images are decomposed into spectrally homogeneous compounds. The resulting compounds are described by their spectral characteristics and optical density. We present the multiplicative physical model of image formation in transmission light microscopy, justify reduction of a hyperspectral image decomposition problem to a blind source separation problem, and provide method for hyperspectral restoration of separated compounds. In our approach, dimensionality reduction using principal component analysis (PCA) is followed by a blind source separation (BSS) algorithm. The BSS method is based on sparsifying transformation of observed images and relative Newton optimization procedure. The presented method was verified on hyperspectral images of biological tissues. The method was compared to the existing approach based on nonnegative matrix factorization. Experiments showed that the presented method is faster and better separates the biological compounds from imaging artifacts. The results obtained in this work may be used for improving automatic microscope hardware calibration and computer-aided diagnostics

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Compressive Sensing and Imaging Applications

Compressive sensing (CS) is a new sampling theory which allows reconstructing signals using sub-Nyquist measurements. It states that a signal can be recovered exactly from randomly undersampled data points if the signal exhibits sparsity in some transform domain (wavelet, Fourier, etc). Instead of measuring it uniformly in a local scheme, signal is correlated with a series of sensing waveforms. These waveforms are so called sensing matrix or measurement matrix. Every measurement is a linear combination of randomly picked signal components. By applying a nonlinear convex optimization algorithm, the original can be recovered. Therefore, signal acquisition and compression are realized simultaneously and the amount of information to be processed is considerably reduced. Due to its unique sensing and reconstruction mechanism, CS creates a new situation in signal acquisition hardware design as well as software development, to handle the increasing pressure on imaging sensors for sensing modalities beyond visible (ultraviolet, infrared, terahertz etc.) and algorithms to accommodate demands for higher-dimensional datasets (hyperspectral or video data cubes). The combination of CS with traditional optical imaging extends the capabilities and also improves the performance of existing equipments and systems. Our research work is focused on the direct application of compressive sensing for imaging in both 2D and 3D cases, such as infrared imaging, hyperspectral imaging and sum frequency generation microscopy. Data acquisition and compression are combined into one step. The computational complexity is passed to the receiving end, which always contains sufficient computer processing power. The sensing stage requirement is pushed to the simplest and cheapest level. In short, simple optical engine structure, robust measuring method and high speed acquisition make compressive sensing-based imaging system a strong competitor to the traditional one. These applications have and will benefit our lives in a deeper and wider way

Compressed sensing in fluorescence microscopy.

Compressed sensing (CS) is a signal processing approach that solves ill-posed inverse problems, from under-sampled data with respect to the Nyquist criterium. CS exploits sparsity constraints based on the knowledge of prior information, relative to the structure of the object in the spatial or other domains. It is commonly used in image and video compression as well as in scientific and medical applications, including computed tomography and magnetic resonance imaging. In the field of fluorescence microscopy, it has been demonstrated to be valuable for fast and high-resolution imaging, from single-molecule localization, super-resolution to light-sheet microscopy. Furthermore, CS has found remarkable applications in the field of mesoscopic imaging, facilitating the study of small animals' organs and entire organisms. This review article illustrates the working principles of CS, its implementations in optical imaging and discusses several relevant uses of CS in the field of fluorescence imaging from super-resolution microscopy to mesoscopy

Hyperspectral Image Unmixing Incorporating Adjacency Information

While the spectral information contained in hyperspectral images is rich, the spatial resolution of such images is in many cases very low. Many pixel spectra are mixtures of pure materials’ spectra and therefore need to be decomposed into their constituents. This work investigates new decomposition methods taking into account spectral, spatial and global 3D adjacency information. This allows for faster and more accurate decomposition results

Mineral identification using data-mining in hyperspectral infrared imagery

Les applications de l’imagerie infrarouge dans le domaine de la géologie sont principalement des applications hyperspectrales. Elles permettent entre autre l’identification minérale, la cartographie, ainsi que l’estimation de la portée. Le plus souvent, ces acquisitions sont réalisées in-situ soit à l’aide de capteurs aéroportés, soit à l’aide de dispositifs portatifs. La découverte de minéraux indicateurs a permis d’améliorer grandement l’exploration minérale. Ceci est en partie dû à l’utilisation d’instruments portatifs. Dans ce contexte le développement de systèmes automatisés permettrait d’augmenter à la fois la qualité de l’exploration et la précision de la détection des indicateurs. C’est dans ce cadre que s’inscrit le travail mené dans ce doctorat. Le sujet consistait en l’utilisation de méthodes d’apprentissage automatique appliquées à l’analyse (au traitement) d’images hyperspectrales prises dans les longueurs d’onde infrarouge. L’objectif recherché étant l’identification de grains minéraux de petites tailles utilisés comme indicateurs minéral -ogiques. Une application potentielle de cette recherche serait le développement d’un outil logiciel d’assistance pour l’analyse des échantillons lors de l’exploration minérale. Les expériences ont été menées en laboratoire dans la gamme relative à l’infrarouge thermique (Long Wave InfraRed, LWIR) de 7.7m à 11.8 m. Ces essais ont permis de proposer une méthode pour calculer l’annulation du continuum. La méthode utilisée lors de ces essais utilise la factorisation matricielle non négative (NMF). En utlisant une factorisation du premier ordre on peut déduire le rayonnement de pénétration, lequel peut ensuite être comparé et analysé par rapport à d’autres méthodes plus communes. L’analyse des résultats spectraux en comparaison avec plusieurs bibliothèques existantes de données a permis de mettre en évidence la suppression du continuum. Les expérience ayant menés à ce résultat ont été conduites en utilisant une plaque Infragold ainsi qu’un objectif macro LWIR. L’identification automatique de grains de différents matériaux tels que la pyrope, l’olivine et le quartz a commencé. Lors d’une phase de comparaison entre des approches supervisées et non supervisées, cette dernière s’est montrée plus approprié en raison du comportement indépendant par rapport à l’étape d’entraînement. Afin de confirmer la qualité de ces résultats quatre expériences ont été menées. Lors d’une première expérience deux algorithmes ont été évalués pour application de regroupements en utilisant l’approche FCC (False Colour Composite). Cet essai a permis d’observer une vitesse de convergence, jusqu’a vingt fois plus rapide, ainsi qu’une efficacité significativement accrue concernant l’identification en comparaison des résultats de la littérature. Cependant des essais effectués sur des données LWIR ont montré un manque de prédiction de la surface du grain lorsque les grains étaient irréguliers avec présence d’agrégats minéraux. La seconde expérience a consisté, en une analyse quantitaive comparative entre deux bases de données de Ground Truth (GT), nommée rigid-GT et observed-GT (rigide-GT: étiquet manuel de la région, observée-GT:étiquetage manuel les pixels). La précision des résultats était 1.5 fois meilleur lorsque l’on a utlisé la base de données observed-GT que rigid-GT. Pour les deux dernières epxérience, des données venant d’un MEB (Microscope Électronique à Balayage) ainsi que d’un microscopie à fluorescence (XRF) ont été ajoutées. Ces données ont permis d’introduire des informations relatives tant aux agrégats minéraux qu’à la surface des grains. Les résultats ont été comparés par des techniques d’identification automatique des minéraux, utilisant ArcGIS. Cette dernière a montré une performance prometteuse quand à l’identification automatique et à aussi été utilisée pour la GT de validation. Dans l’ensemble, les quatre méthodes de cette thèse représentent des méthodologies bénéfiques pour l’identification des minéraux. Ces méthodes présentent l’avantage d’être non-destructives, relativement précises et d’avoir un faible coût en temps calcul ce qui pourrait les qualifier pour être utilisée dans des conditions de laboratoire ou sur le terrain.The geological applications of hyperspectral infrared imagery mainly consist in mineral identification, mapping, airborne or portable instruments, and core logging. Finding the mineral indicators offer considerable benefits in terms of mineralogy and mineral exploration which usually involves application of portable instrument and core logging. Moreover, faster and more mechanized systems development increases the precision of identifying mineral indicators and avoid any possible mis-classification. Therefore, the objective of this thesis was to create a tool to using hyperspectral infrared imagery and process the data through image analysis and machine learning methods to identify small size mineral grains used as mineral indicators. This system would be applied for different circumstances to provide an assistant for geological analysis and mineralogy exploration. The experiments were conducted in laboratory conditions in the long-wave infrared (7.7μm to 11.8μm - LWIR), with a LWIR-macro lens (to improve spatial resolution), an Infragold plate, and a heating source. The process began with a method to calculate the continuum removal. The approach is the application of Non-negative Matrix Factorization (NMF) to extract Rank-1 NMF and estimate the down-welling radiance and then compare it with other conventional methods. The results indicate successful suppression of the continuum from the spectra and enable the spectra to be compared with spectral libraries. Afterwards, to have an automated system, supervised and unsupervised approaches have been tested for identification of pyrope, olivine and quartz grains. The results indicated that the unsupervised approach was more suitable due to independent behavior against training stage. Once these results obtained, two algorithms were tested to create False Color Composites (FCC) applying a clustering approach. The results of this comparison indicate significant computational efficiency (more than 20 times faster) and promising performance for mineral identification. Finally, the reliability of the automated LWIR hyperspectral infrared mineral identification has been tested and the difficulty for identification of the irregular grain’s surface along with the mineral aggregates has been verified. The results were compared to two different Ground Truth(GT) (i.e. rigid-GT and observed-GT) for quantitative calculation. Observed-GT increased the accuracy up to 1.5 times than rigid-GT. The samples were also examined by Micro X-ray Fluorescence (XRF) and Scanning Electron Microscope (SEM) in order to retrieve information for the mineral aggregates and the grain’s surface (biotite, epidote, goethite, diopside, smithsonite, tourmaline, kyanite, scheelite, pyrope, olivine, and quartz). The results of XRF imagery compared with automatic mineral identification techniques, using ArcGIS, and represented a promising performance for automatic identification and have been used for GT validation. In overall, the four methods (i.e. 1.Continuum removal methods; 2. Classification or clustering methods for mineral identification; 3. Two algorithms for clustering of mineral spectra; 4. Reliability verification) in this thesis represent beneficial methodologies to identify minerals. These methods have the advantages to be a non-destructive, relatively accurate and have low computational complexity that might be used to identify and assess mineral grains in the laboratory conditions or in the field

Random access spectral imaging

A salient goal of spectral imaging is to record a so-called hyperspectral data-cube, consisting of two spatial and one spectral dimension. Traditional approaches are based on either time-sequential scanning in either the spatial or spectral dimension: spatial scanning involves passing a fixed aperture over a scene in the manner of a raster scan and spectral scanning is generally based on the use of a tuneable filter, where typically a series of narrow-band images of a fixed field of view are recorded and assembled into the data-cube. Such techniques are suitable only when the scene in question is static or changes slower than the scan rate. When considering dynamic scenes a time-resolved (snapshot) spectral imaging technique is required. Such techniques acquire the whole data-cube in a single measurement, but require a trade-off in spatial and spectral resolution. These trade-offs prevent current snapshot spectral imaging techniques from achieving resolutions on par with time-sequential techniques. Any snapshot device needs to have an optical architecture that allows it to gather light from the scene and map it to the detector in a way that allows the spatial and spectral components can be de-multiplexed to reconstruct the data-cube. This process results in the decreased resolution of snapshot devices as it becomes a problem of mapping a 3D data-cube onto a 2D detector. The sheer volume of data present in the data-cube also presents a processing challenge, particularly in the case of real-time processing. This thesis describes a prototype snapshot spectral imaging device that employs a random-spatial-access technique to record spectra only from the regions of interest in the scene, thus enabling maximisation of integration time and minimisation of data volume and recording rate. The aim of this prototype is to demonstrate how a particular optical architecture will allow for the effect of some of the above mentioned bottlenecks to be removed. Underpinning the basic concept is the fact that in all practical scenes most of the spectrally interesting information is contained in relatively few pixels. The prototype system uses random-spatial-access to multiple points in the scene considered to be of greatest interest. This enables time-resolved high resolution spectrometry to be made simultaneously at points across the full field of view. The enabling technology for the prototype was a digital micromirror device (DMD), which is an array of switchable mirrors that was used to create a two channel system. One channel was to a conventional imaging camera, while the other was to a spectrometer. The DMD acted as a dynamic aperture to the spectrometer and could be used to open and close slits in any part of the spectrometer aperture. The imaging channel was used to guide the selection of points of interest from the scene. An extensive geometric calibration was performed to determine the relationships between the DMD and two channels of the system. Two demonstrations of the prototype are given in this thesis: a dynamic biological scene and a static scene sampled using statistical sampling methods enabled by the dynamic aperture of the system. The dynamic scene consisted of red blood cells in motion and also undergoing a process of de-oxygenation which resulted in a change in the spectrum. Ten red blood cells were tracked across the scene and the expected change in spectrum was observed. For the second example the prototype was modified for Raman spectroscopy by adding laser illumination, a mineral sample was scanned and used to test statistical sampling methods. These methods exploited the re-configurable aperture of the system to sample the scene using blind random sampling and a grid based sampling approach. Other spectral imaging systems have a fixed aperture and cannot operate such sampling schemes