Khalide Jbilou

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one promotes low-rank structure in the solution, while the other one enforces smoothness. To solve the resulting optimization problem, we employ the alternating direction method of multipliers (ADMM). A detailed convergence analysis of the algorithm is provided, and the performance of the methods is demonstrated through a series of numerical experiments.

Foundation models have achieved great success across diverse domains, including remote sensing (RS), thanks to their versatility and strong generalization abilities. However, most RS foundation models are designed for multispectral data, while hyperspectral imagery (HSI) - with its hundreds of spectral bands - remains less explored. Fine-tuning such models for downstream tasks is also challenging, often demanding considerable memory and storage. In this paper, we propose an efficient framework to fine-tune SpectralGPT, a multispectral foundation model, for hyperspectral image classification (HSIC). We explore several Parameter-Efficient Fine-Tuning (PEFT) methods, including Low-Rank Adaptation (LoRA), Kronecker-based adaptation (KronA), Low-Rank Kronecker (LoKr), and the recent LoRA+, which uses distinct learning rates for low-rank adapters scaled by a factor lambda. Inspired by LoRA+, we introduce KronA+, which applies a similar mechanism to the Kronecker matrices. We evaluate our approach on five datasets from different sensors, showing competitive performance with state-of-the-art HSI models. Our full fine-tuning (FFT) setup for SpectralGPT even outperforms a dedicated hyperspectral foundation model on some datasets while requiring only a quarter of the training epochs. Under the same number of epochs, KronA+ reaches similar performance with far fewer trainable parameters - just 0.056 percent - and adds only approximately 0.2 megabytes of storage, making it the most effective PEFT method tested.

Dictionary learning is a widely used technique in signal processing and machine learning that aims to represent data as a linear combination of a few elements from an overcomplete dictionary. In this work, we propose a generalization of the dictionary learning technique using the t-product framework, enabling efficient handling of multidimensional tensor data. We address the dictionary learning problem through online methods suitable for tensor structures. To effectively address the sparsity problem, we utilize an accelerated Iterative Shrinkage-Thresholding Algorithm (ISTA) enhanced with an extrapolation technique known as Anderson acceleration. This approach significantly improves signal reconstruction results. Extensive experiments prove that our proposed method outperforms existing acceleration techniques, particularly in applications such as data completion. These results suggest that our approach can be highly beneficial for large-scale tensor data analysis in various domains.