## 1 Introduction  
The information content within the entire 2D spatial and temporal extent of a dynamic scene cannot be captured and stored using conventional sampling strategies. Modern cameras have sufficient bandwidth to capture megapixel-scale resolution at limited frame rates. However, limited by the size of pixels and the reading circuit of the sensor, the imaging system may suffer motion aliasing caused by lower camera frame frequency or motion blur caused by longer exposure time, when tracking high-speed motion objectives. Compressive sensing (CS) strategies can take advantage of this knowledge by multiplexing high dimensional data stream onto detectors with fewer dimensions, both in terms of frame rate and spatial resolution. To deal with this problem, Coded Aperture Compressive Temporal Imaging (CACTI) [1] was proposed to improve the ability to catch fast-moving targets and serves as an effective measure to record and analyze the key events. It has become an important research direction in Compressive Sensing. CACTI can afford low-cost temporal super-resolution based on the principle of optical field modulation and compressive sensing. The coded aperture is designed to bestow the Restricted Isometry Property (RIP) upon the observation model, to recover the images with high temporal, spectral, spatial or depth resolutions from observed images with limited resolutions; for example, the high-resolution imaging techniques such as focal plane coding, random phase modulation, and coded exposure imaging [2; 3; 4]. To meet the demand on temporal super-resolution imaging, [PERSON] et al. (2015) and [PERSON] et al. (2016) applied the \"flutter shutter\" method to control the shutter within the exposure time with a binary pseudo-random sequence, thus turning the shutter into a broad-band filter. It was expected to overcome the motion aliasing and blur for sampling with low frame frequency, and retain more high-frequency information, to improve the imaging quality and frame frequency. However, the restoration in coded exposure imaging depends on point spread function (PSF) estimation and motion compensation. [PERSON] et al. proposed a coded aperture compressive temporal imager (CACTI) ([PERSON] et al., 2015) that employs temporal mechanical translation of a passive coding element in an intermediate image plane to achieve low power space-time compressive measurement and to demonstrate CACTI's compression and decompression fidelity with 148-frame video reconstructions from single coded images captured with an experimental prototype ([PERSON] et al., 2015). It helps to achieve the high frame frequency for image sequences without the need to modify the performance standards of the imaging devices and integral time, nor of highly precise and fast exposure control, in comparison to hybrid cameras, camera arrays, and Digital Light Processing (DLP) and so on. Since it is more difficult to improve hardware performance, the CACTI has undoubtedly become more promising. However, the reconstructing algorithm considerably affects the CACTI performance, and is closely related to the observing matrix, objective sparsity and compressing ratio. [PERSON] et al. (2016) proposed the application of generalized alternating projection (GAP) in video compressive sensing, which adopts the weighted-\(\ell_{2,1}\) norm to replace \(\ell_{1}\) norm for solving the convex optimization. The reconstruction error of GAP monotonically converges to zero, under a set of group-restricted isometry property (group-RIP) conditions. Thus, GAP is applicable for compressive sensing of natural images and videos. GAP features quick convergence, high calculating efficiency, and anytime convergence property. Most applications, particularly in real systems, utilize GAP to solve the compressive sensing problem in the transformation domain. However, the groups and weights are related to the anticipated importance of wavelet/discrete cosine transform (DCT) coefficients.