Recent investigations have induced relevant advancements of imaging interferometry, which is becoming a viable option for Earth remote sensing. Various research programs have chosen the Sagnac configuration for new imaging interferometers. Due to the growing diffusion of this technique, we have developed a self-contained theory for describing the signal produced by triangular FTSs and its optimal processing. We investigate the relevant disadvantages of multiplexing, and compare dispersive with FTS instruments. The paper addresses some methods for correcting the phase error, and the non-unitary transformation performed by a Sagnac interferometer. The effect of noise on spectral estimations is discussed.

Recent theoretical investigations have shown important radiometric disadvantages of interferential multiplexing in Fourier transform spectrometry that apparently can be applied even to coded aperture spectrometers. We have reexamined the methods of noninterferential multiplexing in order to assess their signal-to-noise ratio (SNR) performance, relying on a theoretical modeling of the multiplexed signals. We are able to show that quite similar SNR and radiometric disadvantages affect multiplex dispersive spectrometry. The effect of noise on spectral estimations is discussed.

The Aerospace Leap-frog Imaging Stationary interferometer for Earth Observation (ALISEO) is a hyperspectral imaging interferometer for Earth remote sensing. The instrument belongs to the class of Sagnac stationary interferometers and acquires the image of the target superimposed to the pattern of autocorrelation functions of the electromagnetic field coming from each pixel. The ALISEO sensor together with the data processing algorithms that retrieve the at-sensor spectral radiance are discussed. A model describing the instrument OPD and interferogram center is also discussed, improving the procedures for phase retrieval and spectral estimation. Images acquired by ALISEO are shown, and examples of retrieved reflectance spectra are presented.

In this paper, we discuss the structure and performance of the maximum entropy temperature-emissivity separation (MaxEnTES) algorithm for assessing land temperature and emissivity from thermal infrared hyperspectral images. This procedure derives the emissivity spectrum and the temperature of the target adopting the maximum entropy (MaxEnt) estimation approach. The main advantage of the MaxEnt statistical inference is the absence of any external hypothesis, which is, instead, the main critical point characterizing any other temperature-emissivity separation (TES) algorithm. The MaxEnTES algorithm carries out the TES task adopting a modified version of the subgradient Shor's r-algorithm adopted for numerical optimization of a MaxEnt objective function. For this purpose, we have utilized the C/C++ Solvopt code from the University of Gratz to develop a practical data processing implementation. In this paper, we discuss the mathematical structure of the MaxEnTES algorithm and analyze its performance in depth using numerical simulations and remote sensing Multispectral Infrared/Visible Imaging Spectrometer images. We show that the MaxEnTES algorithm provides improved accuracy for temperature and emissivity estimation, lowering the standard estimation error to a fraction of degree Kelvin. In agreement with previous investigations, we find that the estimation accuracy grows when increasing the number of available spectral channels. The systematic errors affecting the temperature estimates (e.g., bias) are thoroughly evaluated. We prove that the MaxEnTES algorithm retrieves the correct shape of the target emissivity spectrum even in presence of a significant temperature estimation error.

The increasing amount of data generated by space applications poses several challenges due to limited resources available onboard: power, memory, computation, data rate. In this paper, we propose Compressed Sensing (CS) as the key tool to face those challenges via compressive imaging. This signal processing technique, only recently applied to space applications, dramatically simplifies the image acquisition featuring native compression/encryption and enabling onboard image analysis, allowing to design simpler and lighter optical systems. In this paper, we try to answer the following question: To what extent are the potential benefits of CS going to materialize in a realistic "space big data" application scenario? To this purpose, we first review compressive imaging techniques and already existing prototypes and concepts, critically discussing the technological issues involved. Then, we propose a set of instrument concepts in the application domains of space science, planetary exploration and earth observation, most suitable for a CS-based application. For the most promising of them, we go deeper into the analysis showing preliminary reconstruction performance tests.