Non-convex regularization in remote sensing

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of regularization used and its parametrization. We consider regularization via traditional squared (2) and sparsity-promoting (1) norms, as well as more unconventional nonconvex regularizers (p and Log Sum Penalty). We compare their properties and advantages on several classification and linear unmixing tasks and provide advices on the choice of the best regularizer for the problem at hand. Finally, we also provide a fully functional toolbox for the community.Comment: 11 pages, 11 figure

A Homotopy-based Algorithm for Sparse Multiple Right-hand Sides Nonnegative Least Squares

Nonnegative least squares (NNLS) problems arise in models that rely on additive linear combinations. In particular, they are at the core of nonnegative matrix factorization (NMF) algorithms. The nonnegativity constraint is known to naturally favor sparsity, that is, solutions with few non-zero entries. However, it is often useful to further enhance this sparsity, as it improves the interpretability of the results and helps reducing noise. While the $\ell_0$-"norm", equal to the number of non-zeros entries in a vector, is a natural sparsity measure, its combinatorial nature makes it difficult to use in practical optimization schemes. Most existing approaches thus rely either on its convex surrogate, the $\ell_1$-norm, or on heuristics such as greedy algorithms. In the case of multiple right-hand sides NNLS (MNNLS), which are used within NMF algorithms, sparsity is often enforced column- or row-wise, and the fact that the solution is a matrix is not exploited. In this paper, we first introduce a novel formulation for sparse MNNLS, with a matrix-wise $\ell_0$ sparsity constraint. Then, we present a two-step algorithm to tackle this problem. The first step uses a homotopy algorithm to produce the whole regularization path for all the $\ell_1$-penalized NNLS problems arising in MNNLS, that is, to produce a set of solutions representing different tradeoffs between reconstruction error and sparsity. The second step selects solutions among these paths in order to build a sparsity-constrained matrix that minimizes the reconstruction error. We illustrate the advantages of our proposed algorithm for the unmixing of facial and hyperspectral images.Comment: 20 pages + 7 pages supplementary materia

Assessing and Enabling Independent Component Analysis As A Hyperspectral Unmixing Approach

As a result of its capacity for material discrimination, hyperspectral imaging has been utilized for applications ranging from mining to agriculture to planetary exploration. One of the most common methods of exploiting hyperspectral images is spectral unmixing, which is used to discriminate and locate the various types of materials that are present in the scene. When this processing is done without the aid of a reference library of material spectra, the problem is called blind or unsupervised spectral unmixing. Independent component analysis (ICA) is a blind source separation approach that operates by finding outputs, called independent components, that are statistically independent. ICA has been applied to the unsupervised spectral unmixing problem, producing intriguing, if somewhat unsatisfying results. This dissatisfaction stems from the fact that independent components are subject to a scale ambiguity which must be resolved before they can be used effectively in the context of the spectral unmixing problem. In this dissertation, ICA is explored as a spectral unmixing approach. Various processing steps that are common in many ICA algorithms are examined to assess their impact on spectral unmixing results. Synthetically-generated but physically-realistic data are used to allow the assessment to be quantitative rather than qualitative only. Additionally, two algorithms, class-based abundance rescaling (CBAR) and extended class-based abundance rescaling (CBAR-X), are introduced to enable accurate rescaling of independent components. Experimental results demonstrate the improved rescaling accuracy provided by the CBAR and CBAR-X algorithms, as well as the general viability of ICA as a spectral unmixing approach

Human retinal oximetry using hyperspectral imaging

The aim of the work reported in this thesis was to investigate the possibility of measuring human retinal oxygen saturation using hyperspectral imaging. A direct non-invasive quantitative mapping of retinal oxygen saturation is enabled by hyperspectral imaging whereby the absorption spectra of oxygenated and deoxygenated haemoglobin are recorded and analysed. Implementation of spectral retinal imaging thus requires ophthalmic instrumentation capable of efficiently recording the requisite spectral data cube. For this purpose, a spectral retinal imager was developed for the first time by integrating a liquid crystal tuneable filter into the illumination system of a conventional fundus camera to enable the recording of narrow-band spectral images in time sequence from 400nm to 700nm. Postprocessing algorithms were developed to enable accurate exploitation of spectral retinal images and overcome the confounding problems associated with this technique due to the erratic eye motion and illumination variation. Several algorithms were developed to provide semi-quantitative and quantitative oxygen saturation measurements. Accurate quantitative measurements necessitated an optical model of light propagation into the retina that takes into account the absorption and scattering of light by red blood cells. To validate the oxygen saturation measurements and algorithms, a model eye was constructed and measurements were compared with gold-standard measurements obtained by a Co-Oximeter. The accuracy of the oxygen saturation measurements was (3.31%± 2.19) for oxygenated blood samples. Clinical trials from healthy and diseased subjects were analysed and oxygen saturation measurements were compared to establish a merit of certain retinal diseases. Oxygen saturation measurements were in agreement with clinician expectations in both veins (48%±9) and arteries (96%±5). We also present in this thesis the development of novel clinical instrument based on IRIS to perform retinal oximetry.Al-baath University, Syri

Hyperspectral benthic mapping from underwater robotic platforms

We live on a planet of vast oceans; 70% of the Earth's surface is covered in water. They are integral to supporting life, providing 99% of the inhabitable space on Earth. Our oceans and the habitats within them are under threat due to a variety of factors. To understand the impacts and possible solutions, the monitoring of marine habitats is critically important. Optical imaging as a method for monitoring can provide a vast array of information however imaging through water is complex. To compensate for the selective attenuation of light in water, this thesis presents a novel light propagation model and illustrates how it can improve optical imaging performance. An in-situ hyperspectral system is designed which comprised of two upward looking spectrometers at different positions in the water column. The downwelling light in the water column is continuously sampled by the system which allows for the generation of a dynamic water model. In addition to the two upward looking spectrometers the in-situ system contains an imaging module which can be used for imaging of the seafloor. It consists of a hyperspectral sensor and a trichromatic stereo camera. New calibration methods are presented for the spatial and spectral co-registration of the two optical sensors. The water model is used to create image data which is invariant to the changing optical properties of the water and changing environmental conditions. In this thesis the in-situ optical system is mounted onboard an Autonomous Underwater Vehicle. Data from the imaging module is also used to classify seafloor materials. The classified seafloor patches are integrated into a high resolution 3D benthic map of the surveyed site. Given the limited imaging resolution of the hyperspectral sensor used in this work, a new method is also presented that uses information from the co-registered colour images to inform a new spectral unmixing method to resolve subpixel materials

Topics in High-Dimensional Statistics and the Analysis of Large Hyperspectral Images.

Advancement in imaging technology has made hyperspectral images gathered from remote sensing much more common. The high-dimensional nature of these large scale data coupled with wavelength and spatial dependency necessitates high-dimensional and efficient computation methods to address these issues while producing results that are concise and easy to understand. The thesis addresses these issues by examining high-dimensional methods in the context of hyperspectral image classification, unmixing and wavelength correlation estimation. Chapter 2 re-examines the sparse Bayesian learning (SBL) of linear models in a high-dimensional setting with sparse signal. The hard-thresholded version of the SBL estimator, under orthogonal design, achieves non-asymptotic error rate that is comparable to LASSO. We also establish in the chapter that with high-probability the estimator recovers the sparsity structure of the signal. The ability to recover sparsity structures in high dimensional settings is crucial for unmixing with high-dimensional libraries in the next chapter. In Chapter 3, the thesis investigates the application of SBL on the task of linear/bilinear unmixing and classification of hyperspectral images. The proposed model in this chapter uses latent Markov random fields to classify pixels and account for the spatial dependence between pixels. In the proposed model, the pixels belonging to the same group share the same mixture of pure endmembers. The task of unmixing and classification are performed simultaneously, but this method does not address wavelength dependence. Chapter 4 is a natural extension of the previous chapter that contains the framework to account for both spatial and wavelength dependence in the unmixing of hyperspectral images. The classification of the images are performed using approximate spectral clustering while the unmixing task is performed in tandem with sparse wavelength concentration matrix estimation.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135893/1/chye_1.pd