Abstract--Hyperspectral imaging (HSI) holds great potential for healthcare due to its rich spectral information. However, acquiring HSI data remains costly and technically demanding. Hyperspectral image reconstruction offers a practical solution by recovering HSI data from accessible modalities, such as RGB. While general domain datasets are abundant, the scarcity of human HSI data limits progress in medical applications. T o tackle this, we propose SpectralAdapt, a semi-supervised domain adaptation (SSDA) framework that bridges the domain gap between general and human-centered HSI datasets. T o fully exploit limited labels and abundant unlabeled data, we enhance spectral reasoning by introducing Spectral Density Masking (SDM), which adaptively masks RGB channels based on their spectral complexity, encouraging recovery of informative regions from complementary cues during consistency training. Furthermore, we introduce Spectral Endmember Representation Alignment (SERA), which derives physically interpretable endmembers from valuable labeled pixels and employs them as domain-invariant anchors to guide unlabeled predictions, with momentum updates ensuring adaptability and stability. These components are seamlessly integrated into SpectralAdapt, a spectral prior-guided framework that effectively mitigates domain shift, spectral degradation, and data scarcity in HSI reconstruction. Experiments on benchmark datasets demonstrate consistent improvements in spectral fidelity, cross-domain generalization, and training stability, highlighting the promise of SSDA as an efficient solution for hyperspectral imaging in healthcare.

Neural Radiance Field (NeRF)-based segmentation methods focus on object semantics and rely solely on RGB data, lacking intrinsic material properties. This limitation restricts accurate material perception, which is crucial for robotics, augmented reality, simulation, and other applications. W e introduce UnMix-NeRF, a framework that integrates spectral unmixing into NeRF, enabling joint hy-perspectral novel view synthesis and unsupervised material segmentation. Our method models spectral reflectance via diffuse and specular components, where a learned dictionary of global endmembers represents pure material signatures, and per-point abundances capture their distribution. F or material segmentation, we use spectral signature predictions along learned endmembers, allowing unsupervised material clustering. Additionally, UnMix-NeRF enables scene editing by modifying learned endmember dictionaries for flexible material-based appearance manipulation.

Hyperspectral unmixing aims at estimating material signatures (known as endmembers) and the corresponding proportions (referred to abundances), which is a critical preprocessing step in various hyperspectral imagery applications. This study develops a novel approach called sparsity and total variation (TV) constrained multilayer linear unmixing (STVMLU) for hyperspectral imagery. Specifically, based on a multilayer matrix factorization model, to improve the accuracy of unmixing, a TV constraint is incorporated to consider adjacent spatial similarity. Additionally, a L1/2-norm sparse constraint is adopted to effectively characterize the sparsity of the abundance matrix. For optimizing the STVMLU model, the method of alternating direction method of multipliers (ADMM) is employed, which allows for the simultaneous extraction of endmembers and their corresponding abundance matrix. Experimental results illustrate the enhanced performance of the proposed STVMLU when compared to other algorithms.

Hyperspectral image (HSI) unmixing is a challenging research problem that tries to identify the constituent components, known as endmembers, and their corresponding proportions, known as abundances, in the scene by analysing images captured by hyperspectral cameras. Recently, many deep learning based unmixing approaches have been proposed with the surge of machine learning techniques, especially convolutional neural networks (CNN). However, these methods face two notable challenges: 1. They frequently yield results lacking physical significance, such as signatures corresponding to unknown or non-existent materials. 2. CNNs, as general-purpose network structures, are not explicitly tailored for unmixing tasks. In response to these concerns, our work draws inspiration from double deep image prior (DIP) techniques and algorithm unrolling, presenting a novel network structure that effectively addresses both issues. Specifically, we first propose a MatrixConv Unmixing (MCU) approach for endmember and abundance estimation, respectively, which can be solved via certain iterative solvers. We then unroll these solvers to build two sub-networks, endmember estimation DIP (UEDIP) and abundance estimation DIP (UADIP), to generate the estimation of endmember and abundance, respectively. The overall network is constructed by assembling these two sub-networks. In order to generate meaningful unmixing results, we also propose a composite loss function. To further improve the unmixing quality, we also add explicitly a regularizer for endmember and abundance estimation, respectively. The proposed methods are tested for effectiveness on both synthetic and real datasets.

Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the left matrix captures latent features while the right matrix linearly decomposes the data based on these features. There are many ways to define what makes a component "important." Standard LRMFs, such as the truncated singular value decomposition, focus on minimizing the distance between the original matrix and its low-rank approximation. In this thesis, the notion of "importance" is closely linked to interpretability and uniqueness, which are key to obtaining reliable and meaningful results. This thesis thus focuses on volume-based constraints and regularizations designed to enhance interpretability and uniqueness. We first introduce two new volume-constrained LRMFs designed to enhance these properties. The first assumes that data points are naturally bounded (e.g., movie ratings between 1 and 5 stars) and can be explained by convex combinations of features within the same bounds, allowing them to be interpreted in the same way as the data. The second model is more general, constraining the factors to belong to convex polytopes. Then, two variants of volume-regularized LRMFs are proposed. The first minimizes the volume of the latent features, encouraging them to cluster closely together, while the second maximizes the volume of the decompositions, promoting sparse representations. Across all these models, uniqueness is achieved under the core principle that the factors must be "sufficiently scattered" within their respective feasible sets. Motivated by applications such as blind source separation and missing data imputation, this thesis also proposes efficient algorithms that make these models practical for real-world applications.

Hyperspectral unmixing is the process of determining the presence of individual materials and their respective abundances from an observed pixel spectrum. Unmixing is a fundamental process in hyperspectral image analysis, and is growing in importance as increasingly large spectral libraries are created and used. Unmixing is typically done with ordinary least squares (OLS) regression. However, unmixing with large spectral libraries where the materials present in a pixel are not a priori known, solving for the coefficients in OLS requires inverting a non-invertible matrix from a large spectral library. A number of regression methods are available that can produce a numerical solution using regularization, but with considerably varied effectiveness. Also, simple methods that are unpopular in the statistics literature (i.e. step-wise regression) are used with some level of effectiveness in hyperspectral analysis. In this paper, we provide a thorough performance evaluation of the methods considered, evaluating methods based on how often they select the correct materials in the models. Investigated methods include ordinary least squares regression, non-negative least squares regression, ridge regression, lasso regression, step-wise regression and Bayesian model averaging. We evaluated these unmixing approaches using multiple criteria: incorporation of non-negative abundances, model size, accurate mineral detection and root mean squared error (RMSE). We provide a taxonomy of the regression methods, showing that most methods can be understood as Bayesian methods with specific priors. We conclude that methods that can be derived with priors that correspond to the phenomenology of hyperspectral imagery outperform those with priors that are optimal for prediction performance under the assumptions of ordinary least squares linear regression.

This work proposes a variational inference (VI) framework for hyperspectral unmixing in the presence of endmember variability (HU-EV). An EV-accounted noisy linear mixture model (LMM) is considered, and the presence of outliers is also incorporated into the model. Following the marginalized maximum likelihood (MML) principle, a VI algorithmic structure is designed for probabilistic inference for HU-EV. Specifically, a patch-wise static endmember assumption is employed to exploit spatial smoothness and to try to overcome the ill-posed nature of the HU-EV problem. The design facilitates lightweight, continuous optimization-based updates under a variety of endmember priors. Some of the priors, such as the Beta prior, were previously used under computationally heavy, sampling-based probabilistic HU-EV methods. The effectiveness of the proposed framework is demonstrated through synthetic, semi-real, and real-data experiments.

Hyperspectral imaging technology has a wide range of applications, including forest management, mineral resource exploration, and Earth surface monitoring. Endmember extraction of hyperspectral images is a key step in leveraging this technology for applications. It aims to identifying the spectral signatures of materials, i.e., the major components in the observed scenes. Theoretically speaking, Hottopixx methods should be effective on problems involving extracting endmembers from hyperspectral images. Yet, these methods are challenging to perform in practice, due to high computational costs. They require us to solve LP problems, called Hottopixx models, whose size grows quadratically with the number of pixels in the image. It is thus still unclear as to whether they are actually effective or not. This study clarifies this situation. We propose an efficient and effective implementation of Hottopixx. Our implementation follows the framework of column generation, which is known as a classical but powerful means of solving large-scale LPs. We show in experiments that our implementation is applicable to the endmember extraction from real hyperspectral images and can provide estimations of endmember signatures with higher accuracy than the existing methods can.

Prototypical self-explainable classifiers have emerged to meet the growing demand for interpretable AI systems. These classifiers are designed to incorporate high transparency in their decisions by basing inference on similarity with learned prototypical objects. While these models are designed with diversity in mind, the learned prototypes often do not sufficiently represent all aspects of the input distribution, particularly those in low density regions. Such lack of sufficient data representation, known as representation bias, has been associated with various detrimental properties related to machine learning diversity and fairness. In light of this, we introduce pantypes, a new family of prototypical objects designed to capture the full diversity of the input distribution through a sparse set of objects. We show that pantypes can empower prototypical self-explainable models by occupying divergent regions of the latent space and thus fostering high diversity, interpretability and fairness.

Raman spectroscopy is widely used across scientific domains to characterize the chemical composition of samples in a non-destructive, label-free manner. Many applications entail the unmixing of signals from mixtures of molecular species to identify the individual components present and their proportions, yet conventional methods for chemometrics often struggle with complex mixture scenarios encountered in practice. Here, we develop hyperspectral unmixing algorithms based on autoencoder neural networks, and we systematically validate them using both synthetic and experimental benchmark datasets created in-house. Our results demonstrate that unmixing autoencoders provide improved accuracy, robustness and efficiency compared to standard unmixing methods. We also showcase the applicability of autoencoders to complex biological settings by showing improved biochemical characterization of volumetric Raman imaging data from a monocytic cell.