Fig. 1. Flow chart of proposed method

Fig. 2. Flow chart of NFBM3D algorithm

Fig. 3. Detection results of beam wavefront. (a) Non-uniform distribution of near-field light intensity; (b) spot array image with low signal-to-noise ratio; (c) peak signal-to-noise ratio for each sub-aperture

Fig. 4. Spot array images before and after denoising. (a) Clear image; (b) image with noise; (c) image after NFBM3D denoising

Fig. 5. Average CEE of different methods under different peak signal-to-noise ratios

Fig. 6. CEE of different methods under non-uniformly varying light intensity

Fig. 7. Probability density functions of CEE of different methods under different peak signal-to-noise ratios. (a) Peak signal-to-noise ratio of 3-4; (b) peak signal-to-noise ratio of 4-5

Fig. 8. CEE after pre-processing with different denoising methods under varying light intensity

Fig. 9. Restoration wavefront and restoration residual in absence of noise. (a) Input wavefront; (b) recovery wavefront without noise; (c) recovery residual without noise

Fig. 10. Wavefront recovery residuals after centroid extraction by different methods. (a) TkCoG; (b) Windowing; (c) Adathreshold;(d) NLM; (e) BM3D; (f) NFBM3D

Fig. 11. Experimental system. (a) Schematic diagram; (b) physical map

Fig. 12. Detection results of beam wavefront. (a) Acquired spot array image; (b) peak signal-to-noise ratio of each sub-aperture

Fig. 13. Estimation method for signal-to-noise ratio. (a) Enlarged view of single clear sub-spot; (b) enlarged image of single noisy sub-spot

Fig. 14. CEE of each method

Fig. 15. Input wavefront and recovery wavefronts obtained by different centroid extraction methods. (a) Input wavefront; (b) TkCoG;(c) Windowing; (d) Adathreshold; (e) NLM; (f) VSTBM3D; (g) NFBM3D

Fig. 16. Recovery residuals obtained by different centroid extraction methods. (a) TkCoG; (b) Windowing; (c) Adathreshold; (d) NLM;(e) VSTBM3D; (f) NFBM3D