Algorithms and prototyping of a compressive hyperspectral imager

Compressive sensing (CS) (Candes and Tao 2006) has recently emerged as an efficient technique for sampling a signal with fewer coefficients than dictated by classical Shannon/Nyquist theory. The assumption underlying this approach is that the signal to be sampled must have concise representation on a convenient basis, meaning that there exists a basis where the signal can be expressed with few large coefficients and many (close-to-)zero coefficients. In CS, sampling is performed by taking a number of linear projections of the signal onto pseudorandom sequences, whereas reconstruction exploits knowledge of a domain where the signal is “sparse.” CS has also been used to develop innovative “compressive” imaging systems. A single-pixel camera (Compressive Sensing and Sparse Approximation s.d.) uses a single detector to sequentially acquire random linear measurements of a scene via light modulation. This kind of design is very interesting for imaging at wavelengths beyond the visible light spectrum, where manufacturing detectors is very expensive; CS could be used to design cheaper sensors or sensors providing better resolution for an equal number of detectors. This paradigm is even more appealing for spectral imaging (e.g., Barducci, et al. 2012, 2013, 2014; Magli et al. 2012), where the amount of data generated by the imaging sensor is very large and the system can benefit from a natively compressed imaging format; reconstruction of such large datasets may require ad hoc algorithms in order to fully exploit data redundancies (e.g., Coluccia et al. 2012; Kuiteing et al., 2014). Although compressive hyperspectral imaging has been studied in simulation, there are very few practical implementations; the related background is described in detail in Section 15.1.2. In this chapter, we describe a prototype implementation of a compressive hyperspectral imager, highlighting design, and data quality issues.