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

Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package

Spectral pixels are often a mixture of the pure spectra of the materials, called endmembers, due to the low spatial resolution of hyperspectral sensors, double scattering, and intimate mixtures of materials in the scenes. Unmixing estimates the fractional abundances of the endmembers within the pixel. Depending on the prior knowledge of endmembers, linear unmixing can be divided into three main groups: supervised, semi-supervised, and unsupervised (blind) linear unmixing. Advances in Image processing and machine learning substantially affected unmixing. This paper provides an overview of advanced and conventional unmixing approaches. Additionally, we draw a critical comparison between advanced and conventional techniques from the three categories. We compare the performance of the unmixing techniques on three simulated and two real datasets. The experimental results reveal the advantages of different unmixing categories for different unmixing scenarios. Moreover, we provide an open-source Python-based package available at https://github.com/BehnoodRasti/HySUPP to reproduce the results

Hyperspectral Image Analysis through Unsupervised Deep Learning

Hyperspectral image (HSI) analysis has become an active research area in computer vision field with a wide range of applications. However, in order to yield better recognition and analysis results, we need to address two challenging issues of HSI, i.e., the existence of mixed pixels and its significantly low spatial resolution (LR). In this dissertation, spectral unmixing (SU) and hyperspectral image super-resolution (HSI-SR) approaches are developed to address these two issues with advanced deep learning models in an unsupervised fashion. A specific application, anomaly detection, is also studied, to show the importance of SU.Although deep learning has achieved the state-of-the-art performance on supervised problems, its practice on unsupervised problems has not been fully developed. To address the problem of SU, an untied denoising autoencoder is proposed to decompose the HSI into endmembers and abundances with non-negative and abundance sum-to-one constraints. The denoising capacity is incorporated into the network with a sparsity constraint to boost the performance of endmember extraction and abundance estimation.Moreover, the first attempt is made to solve the problem of HSI-SR using an unsupervised encoder-decoder architecture by fusing the LR HSI with the high-resolution multispectral image (MSI). The architecture is composed of two encoder-decoder networks, coupled through a shared decoder, to preserve the rich spectral information from the HSI network. It encourages the representations from both modalities to follow a sparse Dirichlet distribution which naturally incorporates the two physical constraints of HSI and MSI. And the angular difference between representations are minimized to reduce the spectral distortion.Finally, a novel detection algorithm is proposed through spectral unmixing and dictionary based low-rank decomposition, where the dictionary is constructed with mean-shift clustering and the coefficients of the dictionary is encouraged to be low-rank. Experimental evaluations show significant improvement on the performance of anomaly detection conducted on the abundances (through SU).The effectiveness of the proposed approaches has been evaluated thoroughly by extensive experiments, to achieve the state-of-the-art results

Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements

University of Minnesota Ph.D. dissertation. June 2019. Major: Electrical Engineering. Advisor: Nicholas Sidiropoulos. 1 computer file (PDF); xii, 118 pages.The past few decades have seen a rapid expansion of our digital world. While early dwellers of the Internet exchanged simple text messages via email, modern citizens of the digital world conduct a much richer set of activities online: entertainment, banking, booking for restaurants and hotels, just to name a few. In our digitally enriched lives, we not only enjoy great convenience and efficiency, but also leave behind massive amounts of data that offer ample opportunities for improving these digital services, and creating new ones. Meanwhile, technical advancements have facilitated the emergence of new sensors and networks, that can measure, exchange and log data about real world events. These technologies have been applied to many different scenarios, including environmental monitoring, advanced manufacturing, healthcare, and scientific research in physics, chemistry, bio-technology and social science, to name a few. Leveraging the abundant data, learning-based and data-driven methods have become a dominating paradigm across different areas, with data analytics driving many of the recent developments. However, the massive amount of data also bring considerable challenges for analytics. Among them, the collected data are often high-dimensional, with the true knowledge and signal of interest hidden underneath. It is of great importance to reduce data dimension, and transform the data into the right space. In some cases, the data are generated from certain generative models that are identifiable, making it possible to reduce the data back to the original space. In addition, we are often interested in performing some analysis on the data after dimensionality reduction (DR), and it would be helpful to be mindful about these subsequent analysis steps when performing DR, as latent structures can serve as a valuable prior. Based on this reasoning, we develop two methods, one for the linear generative model case, and the other one for the nonlinear case. In a related setting, we study parameter estimation under unknown nonlinear distortion. In this case, the unknown nonlinearity in measurements poses a severe challenge. In practice, various mechanisms can introduce nonlinearity in the measured data. To combat this challenge, we put forth a nonlinear mixture model, which is well-grounded in real world applications. We show that this model is in fact identifiable up to some trivial indeterminancy. We develop an efficient algorithm to recover latent parameters of this model, and confirm the effectiveness of our theory and algorithm via numerical experiments

MDAS: a new multimodal benchmark dataset for remote sensing

In Earth observation, multimodal data fusion is an intuitive strategy to break the limitation of individual data. Complementary physical contents of data sources allow comprehensive and precise information retrieval. With current satellite missions, such as ESA Copernicus programme, various data will be accessible at an affordable cost. Future applications will have many options for data sources. Such a privilege can be beneficial only if algorithms are ready to work with various data sources. However, current data fusion studies mostly focus on the fusion of two data sources. There are two reasons; first, different combinations of data sources face different scientific challenges. For example, the fusion of synthetic aperture radar (SAR) data and optical images needs to handle the geometric difference, while the fusion of hyperspectral and multispectral images deals with different resolutions on spatial and spectral domains. Second, nowadays, it is still both financially and labour expensive to acquire multiple data sources for the same region at the same time. In this paper, we provide the community with a benchmark multimodal data set, MDAS, for the city of Augsburg, Germany. MDAS includes synthetic aperture radar data, multispectral image, hyperspectral image, digital surface model (DSM), and geographic information system (GIS) data. All these data are collected on the same date, 7 May 2018. MDAS is a new benchmark data set that provides researchers rich options on data selections. In this paper, we run experiments for three typical remote sensing applications, namely, resolution enhancement, spectral unmixing, and land cover classification, on MDAS data set. Our experiments demonstrate the performance of representative state-of-the-art algorithms whose outcomes can serve as baselines for further studies. The dataset is publicly available at https://doi.org/10.14459/2022mp1657312 (Hu et al., 2022a) and the code (including the pre-trained models) at https://doi.org/10.5281/zenodo.7428215 (Hu et al., 2022b)

Factor analysis of dynamic PET images

Thanks to its ability to evaluate metabolic functions in tissues from the temporal evolution of a previously injected radiotracer, dynamic positron emission tomography (PET) has become an ubiquitous analysis tool to quantify biological processes. Several quantification techniques from the PET imaging literature require a previous estimation of global time-activity curves (TACs) (herein called \textit{factors}) representing the concentration of tracer in a reference tissue or blood over time. To this end, factor analysis has often appeared as an unsupervised learning solution for the extraction of factors and their respective fractions in each voxel. Inspired by the hyperspectral unmixing literature, this manuscript addresses two main drawbacks of general factor analysis techniques applied to dynamic PET. The first one is the assumption that the elementary response of each tissue to tracer distribution is spatially homogeneous. Even though this homogeneity assumption has proven its effectiveness in several factor analysis studies, it may not always provide a sufficient description of the underlying data, in particular when abnormalities are present. To tackle this limitation, the models herein proposed introduce an additional degree of freedom to the factors related to specific binding. To this end, a spatially-variant perturbation affects a nominal and common TAC representative of the high-uptake tissue. This variation is spatially indexed and constrained with a dictionary that is either previously learned or explicitly modelled with convolutional nonlinearities affecting non-specific binding tissues. The second drawback is related to the noise distribution in PET images. Even though the positron decay process can be described by a Poisson distribution, the actual noise in reconstructed PET images is not expected to be simply described by Poisson or Gaussian distributions. Therefore, we propose to consider a popular and quite general loss function, called the $\beta$-divergence, that is able to generalize conventional loss functions such as the least-square distance, Kullback-Leibler and Itakura-Saito divergences, respectively corresponding to Gaussian, Poisson and Gamma distributions. This loss function is applied to three factor analysis models in order to evaluate its impact on dynamic PET images with different reconstruction characteristics

Deep Image Prior for Disentangling Mixed Pixels

A mixed pixel in remotely sensed images measures the reflectance and emission from multiple target types (e.g., tree, grass, and building) from a certain area. Mixed pixels exist commonly in spaceborne hyper-/multi-spectral images due to sensor limitations, causing the signature ambiguity problem and impeding high-resolution remote sensing mapping. Disentangling mixed pixels into the underlying constituent components is a challenging ill-posed inverse problem, which requires efficient modeling of spatial prior information and other application-dependent prior knowledge concerning the mixed pixel generation process. The recent deep image prior (DIP) approach and other application-dependent prior information are integrated into a Bayesian framework in the research, which allows comprehensive usage of different prior knowledge. The research improves mixed pixel disentangling using the Bayesian DIP in three key applications: spectral unmixing (SU), subpixel mapping (SPM), and soil moisture product downscaling (SMD). The main contributions are summarized as follows. First, to improve the decomposition of mixed pixels into pure material spectra (i.e., endmembers) and their constituting fractions (i.e., abundances) in SU, a designed deep fully convolutional neural network (DCNN) and a new spectral mixture model (SMM) with heterogeneous noise are integrated into a Bayesian framework that is efficiently solved by a new iterative optimization algorithm. Second, to improve the decomposition of mixed pixels into class labels of subpixels in SPM, a dedicated DCNN architecture and a new discrete SMM are integrated into the Bayesian framework to allow the use of both spatial prior and the forward model. Third, to improve the decomposition of mixed pixels into soil moisture concentrations of subpixels in SMD, a new DIP architecture and a forward degradation model are integrated into the Bayesian framework that is solved by the stochastic gradient descent approach. These new Bayesian approaches improve the state-of-the-art in their respective applications (i.e., SU, SPM, and SMD), which can be potentially utilized for solving other ill-posed inverse problems where simultaneously modeling of the spatial prior and other prior knowledge is needed

Analyse hiérarchique d'images multimodales

There is a growing interest in the development of adapted processing tools for multimodal images (several images acquired over the same scene with different characteristics). Allowing a more complete description of the scene, multimodal images are of interest in various image processing fields, but their optimal handling and exploitation raise several issues. This thesis extends hierarchical representations, a powerful tool for classical image analysis and processing, to multimodal images in order to better exploit the additional information brought by the multimodality and improve classical image processing techniques. %when applied to real applications. This thesis focuses on three different multimodalities frequently encountered in the remote sensing field. We first investigate the spectral-spatial information of hyperspectral images. Based on an adapted construction and processing of the hierarchical representation, we derive a segmentation which is optimal with respect to the spectral unmixing operation. We then focus on the temporal multimodality and sequences of hyperspectral images. Using the hierarchical representation of the frames in the sequence, we propose a new method to achieve object tracking and apply it to chemical gas plume tracking in thermal infrared hyperspectral video sequences. Finally, we study the sensorial multimodality, being images acquired with different sensors. Relying on the concept of braids of partitions, we propose a novel methodology of image segmentation, based on an energetic minimization framework.Il y a un intérêt grandissant pour le développement d’outils de traitements adaptés aux images multimodales (plusieurs images de la même scène acquises avec différentes caractéristiques). Permettant une représentation plus complète de la scène, ces images multimodales ont de l'intérêt dans plusieurs domaines du traitement d'images, mais les exploiter et les manipuler de manière optimale soulève plusieurs questions. Cette thèse étend les représentations hiérarchiques, outil puissant pour le traitement et l’analyse d’images classiques, aux images multimodales afin de mieux exploiter l’information additionnelle apportée par la multimodalité et améliorer les techniques classiques de traitement d’images. Cette thèse se concentre sur trois différentes multimodalités fréquemment rencontrées dans le domaine de la télédétection. Nous examinons premièrement l’information spectrale-spatiale des images hyperspectrales. Une construction et un traitement adaptés de la représentation hiérarchique nous permettent de produire une carte de segmentation de l'image optimale vis-à-vis de l'opération de démélange spectrale. Nous nous concentrons ensuite sur la multimodalité temporelle, traitant des séquences d’images hyperspectrales. En utilisant les représentations hiérarchiques des différentes images de la séquence, nous proposons une nouvelle méthode pour effectuer du suivi d’objet et l’appliquons au suivi de nuages de gaz chimique dans des séquences d’images hyperspectrales dans le domaine thermique infrarouge. Finalement, nous étudions la multimodalité sensorielle, c’est-à-dire les images acquises par différents capteurs. Nous appuyant sur le concept des tresses de partitions, nous proposons une nouvelle méthodologie de segmentation se basant sur un cadre de minimisation d’énergie