Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which exploit the sparsity of signals, have allowed to reconstruct signal and images with less measurements than the traditional Nyquist sensing approach. However, multichannel signals like Hyperspectral images (HSI) have additional structures, like inter-channel correlations, that are not taken into account in the classical CS scheme. In this paper we exploit the linear mixture of sources model, that is the assumption that the multichannel signal is composed of a linear combination of sources, each of them having its own spectral signature, and propose new sampling schemes exploiting this model to considerably decrease the number of measurements needed for the acquisition and source separation. Moreover, we give theoretical lower bounds on the number of measurements required to perform reconstruction of both the multichannel signal and its sources. We also proposed optimization algorithms and extensive experimentation on our target application which is HSI, and show that our approach recovers HSI with far less measurements and computational effort than traditional CS approaches.Comment: 32 page

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Computational Spectral Imaging: A Contemporary Overview

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow identifying objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire the 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where the 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared to conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarises the advances in CSI, starting with SI and its relevance; continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, and the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks

An overview of inverse problem regularization using sparsity

International audienceSparsity constraints are now very popular to regularize inverse problems. We review several approaches which have been proposed in the last ten years to solve inverse problems such as inpainting, deconvolution or blind source separation. We will focus especially on optimization methods based on iterative thresholding methods to derive the solution

COMPRESSIVE SENSING APPROACH TO HYPERSPECTRAL IMAGE COMPRESSION

Hyperspectral image (HSI) processing is one of the key processes in satellite imaging applications. Hyperspectral imaging spectrometers collect huge volumes of data since the image is captured across different wavelength bands in the electromagnetic spectrum. As a result, compression of hyperspectral images is one of the active area in research community from many years. The research work proposes a new compressive sensing based approach for the compression of hyperspectral images called SHSIR (Sparsification of hyperspectral image and reconstruction). The algorithm computes the coefficients of fractional abundance map in matrix setup, which is used to reconstruct the hyperspectral image. To optimize the problem with non-smooth term existence along with large dimensionality, Bregman iterations method of multipliers is used, which converts the difficult optimization problem into simpler cyclic sequence problem. Experimental result demonstrates the supremacy of the proposed method over other existing techniques

スペクトルの線形性を考慮したハイパースペクトラル画像のノイズ除去とアンミキシングに関する研究

This study aims to generalize color line to M-dimensional spectral line feature (M>3) and introduce methods for denoising and unmixing of hyperspectral images based on the spectral linearity.For denoising, we propose a local spectral component decomposition method based on the spectral line. We first calculate the spectral line of an M-channel image, then using the line, we decompose the image into three components: a single M-channel image and two gray-scale images. By virtue of the decomposition, the noise is concentrated on the two images, thus the algorithm needs to denoise only two grayscale images, regardless of the number of channels. For unmixing, we propose an algorithm that exploits the low-rank local abundance by applying the unclear norm to the abundance matrix for local regions of spatial and abundance domains. In optimization problem, the local abundance regularizer is collaborated with the L2, 1 norm and the total variation.北九州市立大

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

Structured Compressed Sensing: From Theory to Applications

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal Processin