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1.INTRODUCTIONCS theory, leveraging the concept of sparsity, affirms that a sparse signal can be efficiently reconstructed by the acquisition of a number of samples far below the minimal one dictated by Nyquist theorem, thus providing a new approach to data acquisition. CS, in fact, permits the design of efficient sensing or sampling protocols that capture the useful information content embedded in a sparse signal and compact it into a small amount of data. Besides the inherent compression of data, CS approach enables the development of novel instrumental concepts, such as the single-pixel camera that can acquire an image using a single photodetector element instead of an array of detectors. The CS approach becomes particularly appealing in those spectral regions where the availability of detector matrices is limited. On the whole, several space applications and related instruments could benefit from the CS approach, with a positive impact on system architecture, detector throughput and downlink bandwidth. This paper presents the results of a study that investigated the potential of CS technologies for optical space instruments in different application domains: Space Science (SS), Planetary Exploration (PE) and Earth Observation (EO). The study was carried out under Optical Compressive Sensing Technologies for Space Applications (OCS-TECH) project funded by European Space Agency (ESA). After a first stage focused on a review of optical CS technology and space applications, the project analyzed in detail two CS-based instrument concepts, each targeting a specific space application: an UV-VIS hyperspectral imager on orbiter for stellar spectrophotometry and a MIR camera for sky observation and real-time detection of NEO. The first instrument relies on a classical CS approach and addresses the reconstruction of the full image; the second instrumental concept explores a novel approach aiming at information extraction without a prior full reconstruction of the image. In this paper, the optical design of the instruments and their critical evaluation is presented. The performance assessment for both instruments is discussed for typical application scenarios by means of simulated data. From the point of view of data reconstruction quality, the results showed a good performance. With reference to system budgets, CS instruments offer some marginal benefits with respect to their traditional counterparts. Most advantages are instead provided in terms of downlink requirements and memory buffer. The knowledge gained during the project also suggested that CS technology can express its best potential when the instrument retrieves information on the acquired data through the use of specific CS signal processing techniques applied directly on-board. 2.STATE OF THE ART2.1State of the art of CS instrumentsCS-based instruments essentially rely on the use of a 2-D Spatial Light Modulator (SLM) - which physically performs a element-by-element product between a random pattern and the incoming light - and of an optical assembly that concentrates the radiation on a single-element detector. In the last few years, several CS-based prototypal instruments have been developed, although the majority of them did not target space applications. The best known CS-prototype is the single-pixel camera developed at Rice University1. The intensive and well-funded research performed at Rice University has fostered the creation of a commercial company, the InView Technology Corporation (http://inviewcorp.com/), that presently produces and commercializes a SWIR camera based on CS technology. The company is also the owner of 23 patents and patent applications inherent to CS instruments development. Another project involving CS technology is the Compressive Optical MONTAGE Photography Initiative (COMP-I) funded under DARPA’s MONTAGE program. The COMP-I project goals are to produce a miniaturized visible and LWIR camera2. The Georgia Institute of Technology has developed an original CS architecture that employs a standard 256x256 CMOS. The sensor and its interface circuitry have been combined with a complex computational circuitry that performs the domain transformation intrinsic in a CS-system3. High spatial and temporal resolutions are obtained in Chen et al.4 by using an array of single pixel cameras that sense in parallel to increase the measurement rate. A proof-of-concept prototype using a sensor with 64× 64 pixels has been developed on this idea. Each sensor pixel is the detector for a single pixel camera, the light modulator being a larger Digital Micromirror Device (DMD), unique for the entire system. A different solution consisting in a lensless compressive imaging is proposed in Huang et al.5 for VIS or IR spectral ranges. At present, there are not commercial CS-based imaging systems for the THz range: nonetheless, a series of prototypal cameras have been developed in the last decade. The major problem is represented by the SLM: DMD and Liquid Crystal Plate (LCP), which have shown great potential from the UV to the NIR, do not operate at longer wavelengths like those of THz domain. Recently, Si- and Ge-based modulators have been used in single pixel camera laboratory prototypes. They are optically controlled through a DMD or electrically driven. An interesting solution that overcomes the problem of low depth modulation is a modulator made up of metamaterials. Single pixel camera prototypes using metamaterials to implement the modulator are reported in Watts et al.6 and Shrekenhamer et al.7. Images of 8x8 pixels have been obtained by CS. Different studies have faced the problem of the application of CS to spectroscopic measurements and in particular to hyperspectral imaging8-12. Results coming from these studies have shown some advantages, but also several problems related to the use of CS in this field, such as the availability of large-size, high speed modulators. Some developments have led to patent registration, like the Tel-Aviv Digital Snapshot Spectral Imager13. Research in developing hyperspectral imaging system with CS technology is driven by the opportunity of reducing the data throughput of sensors, which can be challenging especially for satellite missions. Presently, CS-based instrumentation tailored to space applications has not yet been constructed, except for an ESA-funded study for the development of a laboratory demonstrator of a CS-based hyperspectral imager for Earth Observation11. 2.2State of the art of CS technologyThe key components of a CS-based system are the SLM and the single-element detector. Such components are critical because the performance of the entire system depends on their characteristics. Both the switching speed of SLM and the detector frame rate are key parameters to obtain a good data quality, together with the sensitivity and noise figure of the detector. The SLM is the component that physically implements the random pattern modulations foreseen by CS theory. Since CS paradigm requires the acquisition of a large number of measurements during a given integration time, the SLM must be fast enough to meet such requirement. The number of elements of the SLM is also a crucial parameter that affects the dimensions of the retrieved image. On the other hand, the computational burden for reconstruction algorithms depends on the number of pixels N to be reconstructed for each image. In general, a maximum number of pixels of 512x512 can be considered as a good tradeoff to obtain a good image quality, yet with an acceptable computational burden. Moreover, SLM cryogenic capabilities would be beneficial, especially for infrared spectral range applications. Presently on the market there are three types of programmable SLMs:
The other key element of a CS-based system is the single pixel detector that physically performs the integration. The detector is less critical than the SLM, although high speed, large photosensitive area and low noise are requested for a good performance. Another key feature is the rise time of the detector response, the shorter the rise time the shorter is the time effectively available for a single measurement. In the following, a selection of single pixel detectors suitable for CS applications is listed:
2.3State of the art of CS reconstruction algorithmsSeveral image recovery algorithms from compressive measurements have been proposed in the literature, also for astronomical remote sensing15. They exploit the fact that the image is sparse in a given domain (wavelet, Discrete Cosine Transform (DCT), gradient domain, and so on) and attempt to perform the reconstruction via convex optimization using a l1-norm penalty term16. Although interior point methods can be used to solve this convex optimization problem, they have high computational complexity and run in a time that is asymptotically polynomial (O(N3)) in the number N of image pixels. The most popular method in image reconstruction is to find the image consistent to the acquired data that minimizes the Total Variation (TV) pseudo norm. In Lustig et al.17 the TV minimization is combined with the l1-norm minimization of a sparsifying transform. This approach can be interpreted as requiring the image to be sparse by both the finite differences and the sparsifying transform. To speed up the computation, iterative and greedy algorithms have been proposed to perform the optimization. Greedy algorithms, generally, build up an approximation to the solution one step at a time by making locally optimal choices at each step. One of the most popular greedy algorithms is Orthogonal Matching Pursuit (OMP)18. However, although greedy algorithms are extremely fast, they generally require a larger number of measurements, thereby worsening the CR. 3.INSTRUMENT CONCEPTS FOR SPACE APPLICATIONSA set of CS instrumental concepts showing an expected significant advantage compared to a traditional counterpart system were identified on the basis of the results coming from the review of current space applications and the state of the art for the core component of a CS-based system. The instrumental concepts listed in Table 1 were analyzed, with the aim of identifying the most promising ones. The following parameters were taken into account: available technologies, modulation methods and strategies, instrumental mass and power consumption, number and/or typology of components constituting the system. Data compression expected performance was also preliminarily assessed in terms of expected CR, reconstruction quality and processing time with respect to standard compression procedures. Table 1.List of proposed Instrument Concepts
Amongst these concepts, all the rover-based instruments offer the possibility to increase the total measurement time, and consequently the integration time for a single measure, which is a crucial parameter to obtain a good data quality after CS reconstruction. A CS approach is beneficial for instruments working in spectral regions such as IR e EUV/UV where large matrix detectors are not always available and, in any case, single pixel detectors are definitely cheaper. Several proposed applications are based on a novel approach to CS, relying on the information extraction rather than on a full reconstruction of image/signal. Two out of the fifteen proposed concepts were selected for a preliminary optical design of the CS-based payload. In particular, this paper reports an overview of the preliminary design of a UV-VIS hyperspectral imager on orbiter for stellar spectrophotometry and of a CS-based camera working in the MIR for the on-board detection of NEO. 4.UV-VIS HYPERSPECTRAL IMAGER ON ORBITER FOR STELLAR SPECTROPHOTOMETRYThe proposed CS based instrument is an UV to VIS hyperspectral imager targeting space science applications. The instrument was conceived as an imaging spectrometer/photometer - working in the UV – VIS spectral range - implemented for slitless spectroscopic/photometric astronomy and operating from geostationary or sun-synchronous platform, with characteristics similar to the ones of STIS on Hubble Space Telescope (HST). The acquisition domain for this kind of instruments is highly sparse, thus allowing a good data quality even with high CRs, assuring a significant downlink bandwidth reduction. Moreover, a CS system does not need a compression board with a consequent reduction of system power consumption and mass. A schematic diagram of the instrument is shown in Figure 1. The payload is made up of the following main elements: the telescope, the prism imaging spectrometer, the SLM device, the condenser lens, and the single pixel detector. A Texas Instrument DMD was used as SLM. This device is characterized by micromirrors with a tilt angle of +12°. Data simulation was carried out to evaluate the system performance and data quality after image reconstruction from a set of measurements using OMP18. In Figure 2, the original simulated image with three star spectra and reconstruction results for CR=10 (i.e. a number of measurements equal to 1/10 of the number of pixels of the original image) are reported; Figure 2b shows the original and reconstructed value of each pixel in Figure 2a in raster order. Figure 2b shows a good agreement between original and reconstructed data. This instrument relies on a classical implementation of the CS-techniques, addressing the full reconstruction of the image. 5.MIR CAMERA FOR THE DETECTION OF NEAR EARTH OBJECTSThe proposed instrument is a CS-based camera for sky observations performing on-board detection of moving objects (NEO). This instrument was conceived as a CS-counterpart of the WISE instrument19. This instrument relies on a novel concept that aims at joining a sky survey with image acquisition to the on-board detection of NEO. This approach is different from the classical data-mining and processing of the images at ground. The main advantages offered by this CS architecture consist in the use of a single pixel detector and in the possibility to apply techniques - derived from CS theory - directly on board. The last characteristic permits to obtain information on the NEO presence directly in the measurements domain, without reconstructing the images. The very sparse acquisition domain represented by star fields would permit to achieve high CRs, yet maintaining a good quality of the retrieved information and consequently a considerable downlink bandwidth reduction. Also in this case, the compression board is not needed. The schematic diagram of the proposed optical payload is reported in Figure 3. Figure 3.Schematic layout of the camera operating in the MIR-TIR for sky observations and real time detection of NEO.  The payload consists of the following main elements: a 50-cm telescope, a 512x512 pixel SLM, a condenser lens, a single pixel detector, a proximity electronic board, a temperature controller and coolers. The main drawbacks are the limitations posed by the working temperature of the SLM, which must be higher than 233°K for commercial DMD20. The background emission at such temperature is strong enough to affect the signal of interest, which can be very low. The system should be cooled to cryogenic temperatures in order to reduce the unwanted background contribution. MSA are cryogenic SLM devices, but their frame rate (3-4 Hz) is slow and would require accurate pointing stability of the platform for long time periods to fulfil the requirements of this application. A cryogenic DMD is under development at LAM-CNRS and EPFL20,21, but its size of 32x64 micromirrors is actually too small for this applications. Recent studies have demonstrated that Texas Instrument commercial DMDs can tolerate cryogenic temperature without damage14. The acquisition process was tested using simulated images at the SLM with an operational temperature of 233° K and a procedure that mimics the CS acquisition. Starting from simulated acquisition employing Block Circulant sensing matrices with Circulant Blocks (BCCB), the images are reconstructed by OMP17 by keeping only 10% of samples and exhibit a satisfying quality (Figure 4), although the reconstructed image shows some “noise” due to the presence of background emission. Further tests were made using ad hoc algorithms to detect the NEO without a full reconstruction of the image. 6.CONCLUSIONSThe performance assessment for two instruments based on CS approach has been presented. From the point of view of data reconstruction quality, the results showed a good performance of the designed instruments. With respect to their traditional counterparts however, CS instruments offer only some marginal benefits in terms of mass and power consumption, mainly due to the lack of a compression board. Major advantages are instead provided in terms of downlink requirements and memory buffer. The slitless spectrometer for stellar spectrophotometry adopts a more conservative approach and the technologies needed for its construction are all commercially available, enabling a possible prototype development. The MIR camera for NEO detection instead, although able to exploit the CS potential at its best for its capacity to retrieve information without a full reconstruction of the scene, is expected to operate at cryogenic temperatures to avoid background emission and this requires further development and test activity for key components like the DMD. ACKNOLEDGEMENTSThe OCSTECH project (ITT AO/1-8235/15/NL/RA) was funded under ESA ESTEC contract n. 4000116423/15/NL/BJ/gp. The view expressed in this publication can in no way be taken to reflect the official opinion of the European Space Agency. REFERENCESBrady, D. J., Feldman, M., Pitsianis, N., Guo, J. P., Portnoy, A., & Fiddy, M.,
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