Projected Barzilai–Borwein method for large-scale nonnegative image restoration

Figures & data

Figure 1. Left: true image; Right: blurred noisy image.

Figure 2. Restored images by BB method (left) and PBB method (right) ().

Figure 3. Restored images by PLW method (left) and PG method (right) ().

Figure 4. Restored images by GPCG method (left) () and relative errors for different number of iterations for all algorithms (right).

Table 1. The iteration results for error level

Methods	CPU time (secs)	Number of iterations	Relative error (rerr)	ϵ
PLW	11.897000	7470	0.18380	5.0e  − 5
PG	2.764000	3941	0.13051	1.0e  − 5
BB	0.121000	427	0.15214	1.0e  − 6
PBB	0.521000	796	0.12765	1.0e  − 6
GPCG	1.813000	30	0.14070	0.5

Figure 5. True image.

Figure 6. The blurred images for different noise levels: Left: level = 0.005; Right: level = 0.01.

Figure 7. The blurred images for different noise levels: Left: level = 0.05; Right: level = 0.1.

Figure 8. Restored images by BB method (left) and PBB method (right) (level = 0.005).

Figure 9. Restored images by BB method (left) and PBB method (right) (level = 0.01).

Figure 10. Restored images by BB method (left) and PBB method (right) (level = 0.05).

Figure 11. Restored images by BB method (left) and PBB method (right) (level = 0.1).

Table 2. The iteration results for different noise levels.

Methods	Iteration steps	Number of MVM	Relative error (rerr)	Noise level (level)
BB	140	290	0.0380	0.005
PBB	209	637	0.0358	0.005
GPCG	11	838	0.0358	0.005
BB	168	346	0.0761	0.01
PBB	209	637	0.0700	0.01
GPCG	13	1244	0.0701	0.01
BB	178	366	0.3814	0.05
PBB	204	622	0.2937	0.05
GPCG	11	1092	0.2938	0.05
BB	210	430	0.7629	0.1
PBB	224	682	0.4783	0.1
GPCG	12	1262	0.4783	0.1

Figure 12. Relative errors for different number of iterations for all algorithms (Left: level = 0.005; Right: level = 0.01).

Figure 13. Relative errors for different number of iterations for all algorithms (Left: level = 0.05; Right: level = 0.1).