Abstract
Video spectral imaging technology is an important direction in the development of remote sensing detection. It can achieve 4-dimensional information acquisition （two-dimensional space + spectrum + time）， which is of great significance for application such as dynamic target detection. The current technical means are mainly based on the filter method， and do not have the high-resolution advantage of grating. Uncoupled Slit Array Scan Hyperspectral imager （uSASHI） and Coded Slit Array Scan Hyperspectral imager （cSASHI） are proposed in this paper， both use multiple slits to achieve simultaneous acquisition of multiple fields of view information to improve the information acquisition rate， and enables video-level spectral imaging. The information obtained by each slit of uSASHI will not be coupled， and n slits can achieve n times the improvement of information acquisition efficiency. The slits of cSASHI are arranged according to the compressed sensing theory， which can achieve under-sampling conditions （sampling rate α≤ 1） video spectral imaging， the information acquisition efficiency can be improved by n/α times. The system designed in this paper finally realizes the 1024*490*30 spectral data cube 10 Hz video spectral imaging method， and cSASHI achieves a higher frame rate. The proposed system provides a new direction for the video spectral imaging technology and lays a better foundation for future applications.
The satellite-based hyperspectral imaging technology was one of the important optical remote sensing methods for Earth observation， and it is increasingly recognized by the remote sensing community because of its ability to acquire spectral and image information in three dimensions simultaneously. Hyperspectral imaging systems in traditional remote sensing can be roughly divided into two categories： the push-broom scanning hyperspectral imaging （PSHI） system and the staring hyperspectral imaging （SHI） system. The PSHI system used gratings or prisms， while the SHI system used a tunable optical filter as a splitting device. The latest representative PSHI systems are OSIRIS-REx Visible and Infrared Spectrometer （OVIRS
As the performance requirements of hyperspectral technology gradually increase， it is desired to simultaneously combine high detection sensitivity， high spatial resolution， high spectral resolution， and high temporal resolution. And the above two ways were obviously difficult to achieve. The development of snapshot hyperspectral technology with face-field imaging capability is increasingly focused on， and various new spectroscopic techniques have emerged. It can acquire spatial information and spectral information simultaneously in one sampling period directly or through recovery algorithms. Bowen's integrated field spectral （IFS） imaging technique， based on polygon mirror integration， was the first proposed snapshot spectral imaging concep
This paper firstly intends to propose a slit-scanning hyperspectral imaging （SSHI） system. Instead of being driven by the movement of the platform or scanning mirror， the slit is moved and the one-dimensional spatial information perpendicular to the slit is scanned. This allows the apparatus to detect the in-situ scene while keeping the instrument stationary. On the other hand， the SSHI system has the same components as the PSHI system except for the addition of a moving slit， which maintains the advantage of using a grating， prism， or the like， that is， high spectral resolution can be guaranteed. On this basis， Uncoupled Slit Array Scan Hyperspectral imager（uSASHI）is proposed whose time-resolution is improved. Go a step further， Coded Slit Array Scan Hyperspectral imager（cSASHI）is proposed. Its multiple slits are combined into a coding array， and the system obtains the encoded information of the detection target. Coding is transformed by moving the micro-displacement platform to improve the sampling rate. cSASHI has a similar acquisition and recovery process as the CASSI system. The difference is that we have changed the two-dimensional random coding into the slit’s combination coding， so that the coding board only needs one-dimensional movement. This makes the mathematical model easier to establish as coding complexity becomes lower， and engineering is easier to implement.
The SSHI system is proposed here first. Hyperspectral imaging technology ultimately must acquire two-dimensional spatial information and one-dimensional spectral information. Since existing devices only have two-dimensional detection capability， three-dimensional information acquisition needs to be completed by spatial scanning or temporal scanning. The essence of spatial scanning is the completion of the inter-movement of the target 2D spatial information with the imaging detector. As mentioned above， hyperspectral imagers based on push-broom imaging type are currently the mainstream solution in aerospace. And what they accomplish is the relative motion of the entire imaging system to the target. In fact， in addition to scanning with the help of platform motion or scanning mirror， 3D data cube acquisition can also be achieved by using slit movement scanning. As shown in
Fig. 1 The schematic diagram of the detector display under the slit scanning mode of the SSHI system
图1 SSHI系统狭缝扫描模式下的探测器示意图
SSHI achieves spatial self-scanning， which can eliminate the need for platform pushing and scanning or scanning mirror scanning， and the entire spectral imaging instrument can remain stationary for system detection. The SSHI and PHI can use the same optical components except for the addition of a control module for continuous conversion slit control， i.e.， the high-resolution characteristics of the grating and prism can be maintained. In SSHI， it has step or continuous scanning. For each unit distance the system moves， the two-dimensional information received by the detector （one-dimensional space and one-dimensional spectrum） will move one image element in the corresponding direction， i.e.， the different field-of-view positions of the detection target correspond to different positions in the detector dispersion direction. Ultimately， it is necessary to obtain a data cube by determining the spatial location and spectral position of the spectral data， and then stitching them together.
In the SSHI system， the speed of the slit shift scan is determined by the detector frame frequency and pixel size. If the slit moving speed is v， the detector frame frequency is f， and the pixel size is ， then . This has the same computational relationship as the speed of the platform in PHI.
For a data cube of （horizontal × vertical × spectral）， the slit must be moved N times in the dispersion direction to complete the acquisition of all information. The effective detection area of the detector， i.e.， the specification should be at least . The acquisition time of the whole data cube is for a detector with a frame frequency of . In other words， SSHI can be considered as a video hyperspectral imager with frame frequency detection， which is sufficient for some scenarios.
The SSHI system achieves the acquisition of spectral information at different line-of-view positions by a single slit scan， and one detection time unit corresponds to one line-column field of view. In fact， without changing the optical system and detector system， the scanning efficiency can be greatly improved by changing a single slit into multiple slits and achieving simultaneous scanning of multiple slits to obtain spectral information. The arrangement of the slits ensures that the dispersions corresponding to adjacent slits do not overlap. That is， the interval between the two slits is at least L image elements in size under the condition that the slit-to-detector optical imaging ratio is 1：1， while not considering different dispersions corresponding to different fields of view. Usually， due to reasons such as non-ideal factors of optical components， such as the cut-off wavelength position of the cut-off filter still exists part of the energy. It is necessary to set the adjacent slit interval appropriately larger than L to avoid the occurrence of spectral mixing of different fields of view. The system is called the uncoupled Slit Array Scanning Spectral Imaging System （uSASHI， Uncoupled Slit Array Scan Hyperspectral imager）. The distance between two adjacent slits is D image elements， and there are P slits in the slit array， and there exists the relationship： . The whole slit array only needs to move D image elements to achieve the acquisition of information corresponding to the whole field of view. The scanning efficiency can be improved times compared to SSHI. Apparently， SASHI is a video hyperspectral imaging system with a frame rate of ， which is about times the frame rate of SSHI. Obviously， this is a major enhancement and greatly expands the usefulness of the system.
The SSHI and uSASHI systems have a one-to-one correspondence between the detector image element reception information and the target information， and the information is processed under the Nyquist sampling theorem. In fact， compressive sensing as a novel information processing theory can inspire us to explore new imaging systems. The slit arrays are arranged via a certain coded form rather than at equal intervals， the detector's single acquisition is a superposition of spectral imaging information from multiple slits at different locations. The system maps the 3D data cube onto the 2D detector surface array， forming a mixed stack of encoded information and realizing data dimensionality reduction. The set encoding form corresponds to the detection matrix to be created. The established detection matrix should satisfy the Restricted Isometry property （RIP）， which is necessary to obtain the full information， if it corresponds to the appropriate vectorized detection data. The acquisition of the full spatial spectral image can be achieved by a suitable reconstruction algorithm. The system is called the coded slit array scanning spectral imaging system （cSASHI， Coded Slit Array Scan Hyperspectral imager）.
Since the dispersion only occurs in the horizontal direction， and the vertical direction does not participate in encoding， only one line of data is analyzed for the sake of simplicit
Fig. 2 The process of constructing a solution model
图2 构建方法模型的过程
As shown in
Fig. 3 Comparison of three spectral imaging methods， （a） the slit scanning mode of the SSHI system， （b） the uncoupled slit array scanning of uSASHI， （c） the coded slit array scanning of cSASHI
图3 三种光谱成像方式比较，（a）SSHI，（b）uSASHI，（c） cSASHI
Then：
Written as：
Then：
| . | （1） |
| . | （2） |
When is full rank， it corresponds to a full sampling situation：
| . | （3） |
Which is equivalent to：
| . | （4） |
Under one exposure， cSASHI has the same effective detection area as the SSHI detector. When n coding measurements are performed， the corresponding sample data amount is. The sampling rate is ， and the duration of an entire data cube is n/f. So， cSASHI system can be seen as a hyperspectral video imager with a frame rate detection capability of f/n. As n ≤ N， cSASHI usually has a higher detection frequency than SSHI. It can be seen from the mathematical model that the information obtained by one exposure of the cSASHI system is the linear sum of several single sampling results in SSHI. This guarantees the feasibility of the mathematical model.
It should be noted that the imaging field of view in an optical imaging system is limited， and the design also tends to preserve a better portion of the image quality by limiting the field of view. Therefore， in the encoding system， it is sufficient to ensure that the information in the field of view is encoded. An appropriately sized encoding mask can be set up to match the field-of-view diaphragm so that the encoding sub-region strictly matches the position of the imaging field-of-view region. This subregion is obviously smaller than the area of the mask plate. By moving the mask while the diaphragm， which is used to limit the field of view， remains unchanged， the "code" for the location of the imaging area will change， thus achieving multiple exposures with different codes.
The schematic diagram and mechanical structure design diagram of the 2-imaging experiment system are shown in
Fig. 4 The schematic diagram
图4 系统原理图
Fig. 5 Mechanical design
图5 机械结构设计
The design parameters of this system are shown in the following table.
| Parameters | Panchromatic imaging channel | Spectral imaging channel |
|---|---|---|
| Wavelength | 0.45~0.85 μm | 0.45～0.9 μm |
| Focal length | 1 725 mm | 1 725 mm |
| Working F number | 5.5 | 5.5 |
| Spectral sampling | — | 15 nm |
| Field of view | ±0.370°×±0.278° | ±0.221°×±0.111° |
| Spatial resolution |
0.002 mrad （1 m@500 km） |
0.007 6 mrad （3.8 m@500 km） |
| Spectral resolution | — | 18 nm |
| Spectrometer magnification | — | 1× |
| Detector array size | 6 464×4 852 | 1 024×512 |
| Detector pixel size | 3.45 μm | 13 μm |
The core of the system is the spectral imaging channel， which mainly consists of the spectrometer assembly and the front optical path combined by the telescope and the relay mirror set. In order to meet the specificity of the computational optics， it is necessary to expand the traditional push-scan type line-field spectrometer into a snapshot type face-field spectrometer. At this time， the object surface of the spectrometer is extended in the spectral direction and is rectangular. It also changes from a single slit to a movable array of coded slits， requiring a larger field of view along the track compared to ordinary imaging spectrometers. The parameters of the designed spectrometer components are shown in
| Parameters | Spectrometer components |
|---|---|
| Spectral range | 0.45～0.9 μm |
| Spectrometer magnification | 1× |
| Object size | ±6.656 mm×±3.328 mm |
| Spectroscopic element | Prism pairs |
| Spectral sampling | 15 nm |
| RMS radius of spot | ≤4.5 μm |
| Smile | ＜3.1 μm |
| Keystone | ＜4.2 μm |
| MTF（＠38.46 lp/mm） |
＞0.73＠0.45 μm；＞0.73＠0.65 μm； ＞0.69＠0.9 μm |
Fig. 6 The optical layout of the spectrometer components
图6 光谱仪光学结构
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Fig. 7 Physical view of different types of slits (a) single slit, (b) uniform array slit, (c) coded array slit
图7 不同类型狭缝实物图（a）单狭缝，（b）均匀阵列狭缝，（c）编码阵列狭缝
Fig. 8 Center field spectral calibration results
图8 中心视场光谱定标结果
The image modulation components are realized by laser etching on the chrome-plated quartz substrate， and the etching accuracy can reach 0.1-micron level， which can well meet the system accuracy requirements. At the same time， the quartz substrate has a good optical utilization rate in the visible band， and the chromium layer has a good light blocking effect， so the component has a good contrast performance.
The system still uses the traditional monochromatic parallel light calibration method for spectral calibration. The difference is that this system is a multi-field spectral imaging system in the spectral dimension. The imaging quality and spectral performance of different fields of view are different， and even have great differences， such as the most peripheral field of view and the center field of view. The calibration for each field of view can obtain very accurate calibration data. However， due to the large number of fields of view and the small single-color step size required for calibration， a lot of calibration data will be generated and need post-processing. The central wavelength or bandwidth corresponding to the field of view at different positions in the spectral dimension direction has a certain relationship. This relationship can be easily obtained by linear or nonlinear fitting. Therefore， it is often necessary to select several representative fields of view positions for spectral calibration. The central wavelength or bandwidth of other positions can be linearly interpolated.
The standard monochromator is HORIBA's iHR320 when calibrating， using halogen tungsten lamp as light source， and with parallel light path， the monochromator's light output slit width is 0.1 mm， the scanning step is 0.5 nm， and the wavelength scanning range is 450~900 nm. After calibration， the spectral resolution calibration， and fitting results at the center of the field of view are shown in the figure below.
The system uses multiple slits for surface target imaging. Different positions of the surface target will enter the optical system with different angles of incidence. In order to reduce the influence of dispersion inconsistency， the prism is installed in the optical system at the minimum deflection angle. Position， which is often a way to reduce sensitivity to non-parallelism of incident light rays. The spectral calibration of 5 different fields of view was carried out respectively. From the data fitting effect of center wavelength and spectral resolution， the spectral dispersion characteristics of different fields of view are almost the same.
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（b）
Fig. 9 Spectral calibration results for 5 typical fields of view (a) center wavelength, (b) spectral resolution
图9 五个视场光谱定标结果 (a)中心波长，(b)光谱分辨率
In fact， even with large inconsistencies across different fields of view， spectral position and resolution can be quantified simply by calibration. Another aspect is the quantification and calibration of smile quantification. As shown in the table， the spectral curvature data of the three fields of view are given， and the smile of the system is not very large.
| Slit position | Wavelength | Smile/mm |
|---|---|---|
| Top edge | 450 nm | 0.003 56 |
| 650 nm | 0.002 84 | |
| 850 nm | 0.002 67 | |
| Centre | 450 nm | 0.002 95 |
| 650 nm | 0.004 44 | |
| 850 nm | 0.004 86 | |
| Bottom edge | 450 nm | 0.002 95 |
| 650 nm | 0.004 44 | |
| 850 nm | 0.004 86 |
As for the radiation calibration： It can be seen from the above system model that the corresponding relationship between the received data of the uSASHI detector and the target radiation is clear， just like PHI. The data received by the detector in the cSASHI system is the linear superposition of the corresponding single information elements， so the radiation calibration of the system proposed in this paper has no special requirements with the traditional method.
Small telescopes are used （F#1， f：18 mm） in indoor experiments， to solve and verify problems that may arise in engineering practice.
Synchronized exposure settings for mechanical modulator and detector information acquisition in the proposed system are critical for imaging. The micro motor can have two modes： continuous movement and step movement. In the continuous system mode， the slit continuously scans the image surface of the target， which is like the information acquisition method of traditional PHI. The only difference is that PHI scans the object surface， which does not affect the essential correspondence of information acquisition. In the step movement mode， a detector unit and the ground imaging unit have a clearer one-to-one correspondence， so the system adopts the latter method， and the micro-motor moves one pixel and sends a pulse signal， trigger the detector exposure.
On the other hand， during the imaging process， the movement of the micromotor has non-uniformity， which will lead to non-uniform response of the detector to receive information. The
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Fig. 10 Imaging objectives and preliminary imaging results (a) RGB Image, (b) sampling images, (c) imaging without synchronization correction
图10 成像目标和初步成像结果 (a)彩色图像，(b)采样图像，(c)未经过同步校正的成像结果
An integrating sphere that can be traced to a standard source is used as the illumination source. When the micromotor moves 13 μm， a pulse signal is sent， which is the exposure trigger signal of the detector. The exposure of the detector is completed， and the next unit information acquisition cycle is started. That is， the sampling frame rate Fr of the system depends on the motion period T of the micro-motor and the exposure time τ of the detector： Fr=1/ （T +τ）. In the experiment， the V-408 high-precision motor of PI company is used as the moving part， the maximum moving speed can reach 1.1m/s， and the displacement accuracy can reach 1 μm. By setting the speed， T=1ms is achieved， and τ=9 ms is set according to the brightness of the scene， that is， the system achieves a sampling frame rate of 10 Hz， which is the imaging frame rate of cSASHI， and the imaging frame rate of uSASHI can be higher， as mentioned above.
The reflectivity profiles in different wavelengths are important features for detecting targets. Because the light source is traceable， the reflectivity of the target can be well inverted. As shown in
Fig. 11 Different wavelength images
图11 不同波长图像
（a） Position 1
（b） Position 2
（c） Position 3
（d） Position 4
Fig. 12 Reflectance curves (a)~(d): reflectance curves corresponding to positions 1~4 respectively
图12 反射率曲线(a)~ (d):分别对应位置1~4的反射率曲线
The system is designed for remote sensing applications， and large telescopes are used for long-range imaging， with test targets approximately 500 m away. The panchromatic and spectral channels of the system are simultaneously imaged， and after a simple atmospheric correction， as shown in the figure， the structure of the panchromatic imaging and the imaging results of the 30 spectral channels of uSASHI are given.
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Fig. 13 Outdoor imaging physical picture (a) target in the red box, (b) system physical
图13 室外成像实物图 (a)红框内为目标，(b)系统实物
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Fig. 14 Outdoor panchromatic channel imaging and spectral imaging results (a) panchromatic channel imaging, (b) single-band image of 30 channels
图14 室外全色通道成像和光谱成像结果 (a)全色通道成像，(b) 30个通道的单波段图
Fig. 15 Results of 10 Hz video spectral imaging implemented by uSASHI (a)-(e) are the results of continuous 1s spectral imaging（half of them）
图15 uSASHI实现的10 Hz视频光谱成像结果(a)-(e)为连续1s中的光谱成像结果（其中一半）
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Fig. 16 Spectral imaging results of cSASHI at different sampling rates (a)-(e) Spectral imaging results at 16.6 Hz for 60% sampling rate, 14.3 Hz for 70% sampling rate, 12.5 Hz for 80% sampling rate, 11 Hz for 90% sampling rate, and 10 Hz for 100% sampling rate, respectively
图16 cSASHI不同采样率条件下的光谱成像结果(a)-(e)分别为60%采样率的16.6 Hz, 70%采样率的14.3 Hz, 80%采样率的12.5 Hz, 90%采样率的11 Hz，100% 采样率的10 Hz的光谱成像结果
The spatial resolution of the spectral imaging channel is about 4 times that of the panchromatic channel， and the two channels can realize the complementation of spatial information and spectral information. The spatial resolution of spectral imaging in this experiment is 512×245， and the panchromatic channel achieves 2560×2450 information acquisition. Part of the imaging results are shown in
In summary， we investigated the imaging methods via comparative study of single slit， uncoupled slit arrays， and coded slit arrays. We achieved frame rate 10 Hz for uncoupled slit array spectral imaging and up to 16.6 Hz frame rate transmission characteristics for coded slit array spectral imaging at five sampling rates. The slit array coding is used to replace the line field of view with a surface field of view and to increase the sampling efficiency， ultimately increasing the speed of spectral imaging of external dynamic targets，A new type of spectral imaging system was then realized. The system proposed in this paper uses a prism as the spectroscopic device， which can be replaced by a grating or a combination of the two in future research， retaining the advantages of high spectral resolution of the spectroscopic device to accommodate more applications. The essence of uSASHI is to collect and process information under the traditional information processing framework. It can realize flexible conversion of spatial， spectral and temporal resolutions by adjusting system parameter settings. It is suitable for application scenarios that require high reliability of remote sensing data. cSASHI is based on the sparsity of imaging data， information acquisition under the framework of compressed sensing， an emerging information theory， can achieve higher data acquisition efficiency than uSASHI， and will lose some detailed information， but can retain the principal component information of the target， which is suitable for dynamic targets， scenarios such as tracking and recognition， which do not require complete information. In addition， the modulation component of the system acquires information by scanning， which can achieve good information acquisition for static targets， but it is unavoidable that there will be problems caused by the difference in scanning time for dynamic target scenes. The adjustment of the synchronization method of detector acquisition and modulator can improve this problem and is also one of the future research directions.
References
Reuter D C， Simon A A， Hair J， et al. The OSIRIS-REx Visible and Infrared Spectrometer （OVIRS）： Spectral Maps of the Asteroid Bennu ［J］. Space Science Reviews， 2017， 214（54）： 1-22. 10.1007/s11214-018-0482-9 [Baidu Scholar]
Liu Y. Visible-shortwave Infrared Hyperspectral Imager of GF-5 Satellite ［J］. Spacecraft Recovery & Remote Sensing， 2018， 39（03）：25-28. [Baidu Scholar]
刘银年. “高分五号”卫星可见短波红外高光谱相机的研制［J］. 航天返回与遥感， 2018， 39（03）： 25-28. [Baidu Scholar]
Bibring J P， Hamm V， Langevin Y， et al. The MicrOmega Investigation Onboard Hayabusa2 ［J］. Space Science Reviews， 2017， 208（29）： 401-412. 10.1007/s11214-017-0335-y [Baidu Scholar]
Li C， Liu D， Liu B， et al. Chang'E- 4 initial spectroscopic identification of lunar far-side mantle-derived materials ［J］. Nature， 2019， 569（7756）： 378-382. 10.1038/s41586-019-1189-0 [Baidu Scholar]
Gao Z D， Gao H X， Zhu Y Y， et al. Review of snapshot spectral imaging technologies ［J］. Optics and Precision Engineering， 2020， 28（6）：1323-1343. [Baidu Scholar]
高泽东， 高洪兴， 朱院院， 等. 快照式光谱成像技术综述［J］. 光学精密工程， 2020， 28（6）：1323-1343. [Baidu Scholar]
Okamoto T， Yamaguchi I. Simultaneous acquisition of spectral image information ［J］. Optics Letters， 1991， 16（16）： 1277-1279. 10.1364/ol.16.001277 [Baidu Scholar]
Ford B， Descour M， Lynch R. Large-image-format computed tomography imaging spectrometer for fluorescence microscopy ［J］. Optics Express， 2001， 9（9）： 444-453. 10.1364/oe.9.000444 [Baidu Scholar]
Kudenov M W， Dereniak E L. Compact snapshot birefringent imaging Fourier transform spectrometer ［J］. Proceedings of SPIE - The International Society for Optical Engineering， 2010， 781206. 10.1117/12.864703 [Baidu Scholar]
Allington-Smith J. Basic principles of integral field spectroscopy ［J］. New Astronomy Reviews， 2006， 50（4/5）： 244-251. 10.1016/j.newar.2006.02.024 [Baidu Scholar]
Bodkin A， Sheinis A， Norton A， et al. Snapshot hyperspectral imaging： the hyper pixel array camera ［J］. Proceedings of SPIE - The International Society for Optical Engineering， 2009， 73340H. 10.1117/12.818929 [Baidu Scholar]
Wang Y， Pawlowski M E， Tkaczyk T S. High spatial sampling light-guide snapshot spectrometer ［J］. Optical Engineering， 2017， 56（8）： 081803. 10.1117/1.oe.56.8.081803 [Baidu Scholar]
Mu T， Han F， Bao D， et al. Compact snapshot optically replicating and remapping imaging spectrometer （ORRIS） using a focal plane continuous variable filter ［J］. Optics Letters， 2019， 44（5）： 1281-1284. 10.1364/ol.44.001281 [Baidu Scholar]
Donoho D L. Compressed sensing ［J］. IEEE Transactions on Information Theory， 2006， 52（4）： 1289-1306. 10.1109/tit.2006.871582 [Baidu Scholar]
Candes E J， Romberg J， Tao T. Robust uncertainty principles： exact signal reconstruction from highly incomplete frequency information ［J］. IEEE Transactions on Information Theory， 2006， 52（2）： 489-509. 10.1109/tit.2005.862083 [Baidu Scholar]
Wagadarikar A A， Bones P J， Fiddy M A， et al. SPIE Proceedings ［SPIE Optical Engineering + Applications - San Diego， California， USA （Sunday 10 August 2008）］ Image Reconstruction from Incomplete Data V - Spectral image estimation for coded aperture snapshot spectral imagers ［J］. 2008， 707602. 10.1117/12.795545 [Baidu Scholar]
Kittle D， Choi K， Wagadarikar A， et al. Multiframe image estimation for coded aperture snapshot spectral imagers ［J］. Applied Optics， 2010， 49（36）： 6824-6833. 10.1364/ao.49.006824 [Baidu Scholar]
Gehm M E， John R， Brady D J， et al. Single-shot compressive spectral imaging with a dual-disperser architecture ［J］. Optics Express， 2007， 15（21）： 14013-14027. 10.1364/oe.15.014013 [Baidu Scholar]
Sun T， Kelly K. Compressive sensing hyperspectral imager ［C］. Computational Optical Sensing and Imaging. Optical Society of America， 2009： CTuA5. 10.1364/cosi.2009.ctua5 [Baidu Scholar]
August Y， Vachman C， Rivenson Y， et al. Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains ［J］. Applied Optics， 2013， 52（10）： 46-54. 10.1364/ao.52.000d46 [Baidu Scholar]
Liu S J， Zhang X D， Zhang Y， et al. Multi-frame image coded aperture snapshot spectral image technology ［J］. Journal of Infrared and Millimeter Waves， 2017， 36（6）： 799-804. [Baidu Scholar]
Sun J， Wang S， Dong Y. Sparse block circulant matrices for compressed sensing ［J］. Iet Communications， 2013， 7（13）： 1412-1418. 10.1049/iet-com.2013.0030 [Baidu Scholar]
Chartrand R， Yin W. Iteratively reweighted algorithms for compressive sensing ［C］. IEEE International Conference on Acoustics， Speech and Signal Processing， 2008. 10.1109/icassp.2008.4518498 [Baidu Scholar]