Exploiting Structural Complexity for Robust and Rapid Hyperspectral Imaging

This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by this we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization operation without prior knowledge of the noisy bands. This result is novel for for hyperspectral imaging applications. In addition, we show that imaging for the Computed Tomography Imaging Systems (CTIS) can be improved under limited angle tomography by using low-rank penalization. For both of these cases we exploit the recent results in the theory of low-rank matrix completion using nuclear norm minimization

Sparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman iterative techniques

2012 Fall.Includes bibliographical references.In this dissertation we propose Split Bregman algorithms for several multivariate analytic techniques for dimensionality reduction and feature selection including Sparse Principal Components Analysis, Bisparse Singular Value Decomposition (BSSVD) and Bisparse Singular Value Decomposition with an ℓ1-constrained classifier BSSVDℓ1. For each of these problems we construct and solve a new optimization problem using these Bregman iterative techniques. Each of the proposed optimization problems contain one or more ℓ1-regularization terms to enforce sparsity in the solutions. The use of the ℓ1-norm to enforce sparsity is a widely used technique, however, its lack of differentiability makes it more difficult to solve problems including these types of terms. Bregman iterations make these solutions possible without the addition of variables and algorithms such as the Split Bregman algorithm makes additional penalty terms and multiple ℓ1 terms feasible, a trait that is not present in other state of the art algorithms such as the fixed point continuation algorithm. It is also shown empirically to be faster than another iterative solver for total variation image denoising, another ℓ1-regularized problem, in. We also link sparse Principal Components to cluster centers, denoise Hyperspectral Images using the BSSVD, identify and remove ambiguous observations from a classification problem using the algorithm and detect anomalistic subgraphs using Sparse Eigenvectors of the Modularity Matrix

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS

Discriminative variable selection for clustering with the sparse Fisher-EM algorithm

The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results. Existing approaches have demonstrated the efficiency of variable selection for clustering but turn out to be either very time consuming or not sparse enough in high-dimensional spaces. This work proposes to perform a selection of the discriminative variables by introducing sparsity in the loading matrix of the Fisher-EM algorithm. This clustering method has been recently proposed for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a low-dimensional discriminative subspace. Three different approaches are proposed in this work to introduce sparsity in the orientation matrix of the discriminative subspace through $\ell_{1}$-type penalizations. Experimental comparisons with existing approaches on simulated and real-world data sets demonstrate the interest of the proposed methodology. An application to the segmentation of hyperspectral images of the planet Mars is also presented

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

Deep Hyperspectral and Multispectral Image Fusion with Inter-image Variability

Hyperspectral and multispectral image fusion allows us to overcome the hardware limitations of hyperspectral imaging systems inherent to their lower spatial resolution. Nevertheless, existing algorithms usually fail to consider realistic image acquisition conditions. This paper presents a general imaging model that considers inter-image variability of data from heterogeneous sources and flexible image priors. The fusion problem is stated as an optimization problem in the maximum a posteriori framework. We introduce an original image fusion method that, on the one hand, solves the optimization problem accounting for inter-image variability with an iteratively reweighted scheme and, on the other hand, that leverages light-weight CNN-based networks to learn realistic image priors from data. In addition, we propose a zero-shot strategy to directly learn the image-specific prior of the latent images in an unsupervised manner. The performance of the algorithm is illustrated with real data subject to inter-image variability.Comment: IEEE Trans. Geosci. Remote sens., to be published. Manuscript submitted August 23, 2022; revised Dec. 15, 2022, and Mar. 13, 2023; and accepted Apr. 07, 202