A Two-step Linear Mixing Model for Unmixing under Hyperspectral Variability

• URL: http://arxiv.org/abs/2502.17212v2
• Date: Tue, 18 Mar 2025 08:05:10 GMT
• Title: A Two-step Linear Mixing Model for Unmixing under Hyperspectral Variability
• Authors: Xander Haijen, Bikram Koirala, Xuanwen Tao, Paul Scheunders,
• Abstract summary: Spectral unmixing is an important task in the research field of hyperspectral image processing.<n>The Linear Mixing Model has received an attention due to its simplicity and ease of use.<n>We show that the model is competitive and in some cases superior to existing well-established unmixing methods.
• Score: 1.6061490167492505
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Spectral unmixing is an important task in the research field of hyperspectral image processing. It can be thought of as a regression problem, where the observed variable (i.e., an image pixel) is to be found as a function of the response variables (i.e., the pure materials in a scene, called endmembers). The Linear Mixing Model (LMM) has received a great deal of attention, due to its simplicity and ease of use in, e.g., optimization problems. Its biggest flaw is that it assumes that any pure material can be characterized by one unique spectrum throughout the entire scene. In many cases this is incorrect: the endmembers face a significant amount of spectral variability caused by, e.g., illumination conditions, atmospheric effects, or intrinsic variability. Researchers have suggested several generalizations of the LMM to mitigate this effect. However, most models lead to ill-posed and highly non-convex optimization problems, which are hard to solve and have hyperparameters that are difficult to tune. In this paper, we propose a two-step LMM that bridges the gap between model complexity and computational tractability. We show that this model leads to only a mildly non-convex optimization problem, which we solve with an interior-point solver. This method requires virtually no hyperparameter tuning, and can therefore be used easily and quickly in a wide range of unmixing tasks. We show that the model is competitive and in some cases superior to existing and well-established unmixing methods and algorithms. We do this through several experiments on synthetic data, real-life satellite data, and hybrid synthetic-real data.

Related papers

• Predictable Scale: Part I -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining [56.58170370127227]
  We show that optimal learning rate follows a power-law relationship with both model parameters and data sizes, while optimal batch size scales primarily with data sizes. This work is the first work that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers.
  arXiv  Detail & Related papers  (2025-03-06T18:58:29Z)
• Go With the Flow: Fast Diffusion for Gaussian Mixture Models [16.07896640031724]
  Schrodinger Bridges (SBs) are diffusion processes that steer in finite time, a given initial distribution to another final one while minimizing a suitable cost functional.<n>We propose an analytic parametrization of a set of feasible policies for solving low dimensional problems.<n>We showcase the potential of this approach in low-to-image problems such as image-to-image translation in the latent space of an autoencoder, learning of cellular dynamics using multi-marginal momentum SB problems and various other examples.
  arXiv  Detail & Related papers  (2024-12-12T08:40:22Z)
• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• SMILE: Zero-Shot Sparse Mixture of Low-Rank Experts Construction From Pre-Trained Foundation Models [85.67096251281191]
  We present an innovative approach to model fusion called zero-shot Sparse MIxture of Low-rank Experts (SMILE) construction. SMILE allows for the upscaling of source models into an MoE model without extra data or further training. We conduct extensive experiments across diverse scenarios, such as image classification and text generation tasks, using full fine-tuning and LoRA fine-tuning.
  arXiv  Detail & Related papers  (2024-08-19T17:32:15Z)
• Sensitivity analysis using the Metamodel of Optimal Prognosis [0.0]
  In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models. We present an automatic approach for the selection of the optimal suitable meta-model for the actual problem.
  arXiv  Detail & Related papers  (2024-08-07T07:09:06Z)
• Merging Multi-Task Models via Weight-Ensembling Mixture of Experts [64.94129594112557]
  Merging Transformer-based models trained on different tasks into a single unified model can execute all the tasks concurrently. Previous methods, exemplified by task arithmetic, have been proven to be both effective and scalable. We propose to merge most of the parameters while upscaling the Transformer layers to a weight-ensembling mixture of experts (MoE) module.
  arXiv  Detail & Related papers  (2024-02-01T08:58:57Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Sliced gradient-enhanced Kriging for high-dimensional function approximation [2.8228516010000617]
  Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. It tends to get impractical for high-dimensional problems due to the size of the inherent correlation matrix. A new method, called sliced GE-Kriging (SGE-Kriging), is developed in this paper for reducing the size of the correlation matrix. The results show that the SGE-Kriging model features an accuracy and robustness that is comparable to the standard one but comes at much less training costs.
  arXiv  Detail & Related papers  (2022-04-05T07:27:14Z)
• Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems [4.280301926296439]
  In this work, we explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver. DeepONet is trained offline using data acquired from the fine solver for learning the underlying and possibly unknown fine-scale dynamics. We present various benchmarks to assess accuracy and speedup, and in particular we develop a coupling algorithm for a time-dependent problem.
  arXiv  Detail & Related papers  (2022-02-25T20:46:08Z)
• Minimizing Entropy to Discover Good Solutions to Recurrent Mixed Integer Programs [0.0]
  Current solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. Recent works have shown that machine learning (ML) can be integrated with an MIP solver to inject domain knowledge and efficiently close the optimality gap. This paper proposes an online solver that uses the notion of entropy to efficiently build a model with minimal training data and tuning.
  arXiv  Detail & Related papers  (2022-02-07T18:52:56Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• PCA Reduced Gaussian Mixture Models with Applications in Superresolution [1.885698488789676]
  This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture Model in conjunction with a reduction of the dimensionality of the data in each component of the model. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob.
  arXiv  Detail & Related papers  (2020-09-16T07:33:56Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.