The diagnosis technology of laser-driven inertial confinement fusion (ICF) is an essential research direction to promote the development of controllable nuclear fusion. Specifically, the velocity interferometer system for any reflector (VISAR) is the most extensively employed diagnostic device of ICF, and it is adopted to record one-dimensional wavefront information with picosecond time resolution generated by ICF. However, the information is only confined to the velocity changes of a line on the target surface and cannot provide two-dimensional (2D) velocity field information of all locations on the target surface. A new type of 2D-VISAR diagnosis system is obtained by combining the compressed ultra-fast photography (CUP) system which can implement 2D ultra-fast imaging with line-VISAR and is applied to ICF diagnosis. The compressed 2D images with high time resolution are obtained, and the 2D stripes of time-varying shock waves are obtained by the inversion algorithm. However, the current mainstream inversion algorithms are readily affected by their regularization parameters, with unstable imaging effects. Therefore, we propose a compressed image inversion algorithm based on variable-accelerated generalized alternating projection (GAP) to optimize the CUP-VISAR inversion effect.

We put forward a novel CUP-VISAR compressed image inversion algorithm. First, considering the strong low-rank and gradient sparsity characteristics of 2D fringe images, low rank (LR) regularization and total variation (TV) regularization are employed as the prior information of image processing, and the problem is transformed into an optimization problem based on double prior constraints of LR and TV. The GAP algorithm is utilized as an iterative solution framework to decompose the objective optimization problem into two sub-problems, and TV and LR are extended to the sub-problems respectively to give full expression to the synergistic effect of double prior constraints. Finally, considering the influence of error accumulation in iterative GAP under chaotic images, the structure of the algorithm is optimized and improved, and the variable-accelerated processing is proposed to reduce iterative error accumulation.

In the simulation experiment, the shock wave velocity recorded by line-VISAR is extracted to generate a 2D simulation image (Fig. 3). Furthermore, the 2D-VISAR simulation fringe image is extended in the time dimension as the original data (Fig. 4), which is encoded, chopped and compressed to obtain a 2D image with 60 compressed frames (Fig. 6). The inversion effect is simulated and contrasted in noise-free and noisy environments. The results show that compared with the existing algorithms, the average peak signal-to-noise ratio of the proposed algorithm is increased by 11.0 dB and the average structural similarity is increased by 11.4% in the case of no noise (Fig. 8). In the case of noise, the algorithm has stable inversion effect and sound anti-noise ability (Table 1 and Fig. 9). In the real experiment, the experimental optical path is set up (Fig. 10), the CUP-VISAR branch system is adopted to obtain coded images and 2D compressed images, and the line-VISAR branch system is leveraged to obtain 1D shock wave velocity data as the experimental control group (Fig. 11). In the CUP system, the DMD coding aperture is 8×8, the stripe camera slit is entirely opened (about 5 mm), and the temporal resolution is 200 ns. Pulse width of the probe is 5 ns, the image detection frame rate is 5 frames/ns, and the pixel size of the compressed image is 349×788, with the number of compressed frames being 25. The results show that compared with the actual compressed images, the proposed algorithm can still invert the 2D shock wave periphery with clear contour (Figs. 12 and 13). The inversion results are transformed into line-VISAR images and the one-dimensional shock wave velocity is extracted for comparison. Compared with that of the line-VISAR shock wave velocity, the maximal relative error of the inversion results of the proposed algorithm decreases from 20.38% to 11.66%, with a reduction of 8.72% (Fig. 15).

In the proposed CUP-VISAR compressed image inversion algorithm, we introduce LR and TV regularization terms according to the characteristics of fringe images and build a double prior constraint optimization model to promote piecewise smoothing and preserve image features and details. Then, we utilize the GAP framework to solve the optimization model iteratively. Finally, we propose a variable-accelerated method to enhance the anti-noise ability of the algorithm for addressing the error accumulation problem caused by noise factors in GAP iteration. The experimental results show that the proposed algorithm performs well in subjective visual and objective evaluation parameters for the inversion quality of CUP-VISAR compressed images. This means that the algorithm can retain image structure details and smooth characteristics, with sound denoising performance, which verifies the feasibility of the proposed algorithm in CUP-VISAR.