Hyperspectral remote sensing technology has advanced significantly in the past two decades. Current sensors onboard airborne and spaceborne platforms cover large areas of the Earth surface with unprecedented spectral, spatial, and temporal resolutions. These characteristics enable a myriad of applications requiring fine identification of materials or estimation of physical parameters. Very often, these applications rely on sophisticated and complex data analysis methods. The sources of difficulties are, namely, the high dimensionality and size of the hyperspectral data, the spectral mixing (linear and nonlinear), and the degradation mechanisms associated to the measurement process such as noise and atmospheric effects. This paper presents a tutorial/overview cross section of some relevant hyperspectral data analysis methods and algorithms, organized in six main topics: data fusion, unmixing, classification, target detection, physical parameter retrieval, and fast computing. In all topics, we describe the state-of-the-art, provide illustrative examples, and point to future challenges and research directions.

We conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets: (1) the wavelet histogram signatures which capture all first order statistics using a model based approach and (2) the wavelet co-occurrence signatures, which reflect the coefficients' second-order statistics. The introduced feature sets outperform the traditionally used energy. Best performance is achieved by combining histogram and co-occurrence signatures.

Hyperspectral remote sensing is based on measuring the scattered and reflected electromagnetic signals from the Earth’s surface emitted by the Sun. The received radiance at the sensor is usually degraded by atmospheric effects and instrumental (sensor) noises which include thermal (Johnson) noise, quantization noise, and shot (photon) noise. Noise reduction is often considered as a preprocessing step for hyperspectral imagery. In the past decade, hyperspectral noise reduction techniques have evolved substantially from two dimensional bandwise techniques to three dimensional ones, and varieties of low-rank methods have been forwarded to improve the signal to noise ratio of the observed data. Despite all the developments and advances, there is a lack of a comprehensive overview of these techniques and their impact on hyperspectral imagery applications. In this paper, we address the following two main issues; (1) Providing an overview of the techniques developed in the past decade for hyperspectral image noise reduction; (2) Discussing the performance of these techniques by applying them as a preprocessing step to improve a hyperspectral image analysis task, i.e., classification. Additionally, this paper discusses about the hyperspectral image modeling and denoising challenges. Furthermore, different noise types that exist in hyperspectral images have been described. The denoising experiments have confirmed the advantages of the use of low-rank denoising techniques compared to the other denoising techniques in terms of signal to noise ratio and spectral angle distance. In the classification experiments, classification accuracies have improved when denoising techniques have been applied as a preprocessing step.

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR.

In hyperspectral unmixing, bilinear and linear-quadratic models have become popular recently, and also the polynomial postnonlinear model shows promising results. These models do not consider endmember interactions involving more than two endmembers, although such interactions might compose a nontrivial part of the observed spectrum in scenarios involving bright materials and complex geometrical structures, such as vegetation and intimate mixtures. In this paper, we present an extension of these models to include an infinite number of interactions. Several technical problems, such as divergence of the resulting series, can be avoided by introducing an optical interaction probability, which becomes the only free parameter of the model in addition to the abundances. We present an unmixing strategy based on this multilinear mixing (MLM) model; present comparisons with the bilinear models and the Hapke model for intimate mixing; and show that, in several scenarios, the MLM model obtains superior results.