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where [mathematical expression not reproducible], and [mathematical expression not reproducible] denote the denoised image obtained by the CGTV, CPA, SpB, and PDHG algorithms, respectively.
Image SNR [lambda] PSNR(f) PSNR(u[lambda]) [R.sub.e](u[lambda]) 2.5 0.022 19.186 30.663 7.200x[10.sup.-2] Lena 5 0.020 21.689 31.771 6.338x[10.sup.-2] 7.5 0.017 24.186 32.425 5.878x[10.sup.-2] 2.5 0.015 15.905 26.313 8.148x[10.sup.-2] Boat 5 0.014 18.405 27.169 7.384x[10.sup.-2] 7.5 0.012 20.904 27.620 7.009x[10.sup.-2] 2.5 0.010 11.602 24.897 1.029x[10.sup.-1] Cat 5 0.009 14.102 25.887 9.190x[10.sup.-2] 7.5 0.008 16.602 26.757 8.786x[10.sup.-2] 2.5 0.017 17.072 27.227 9.142x[10.sup.-2] Man 5 0.016 19.572 28.044 8.321x[10.sup.-2] 7 0.014 22.072 28.442 7.949x[10.sup.-2] Image CPU-time 1.97s Lena 4.31s 3.46s 3.920s Boat 2.95s 3.77s 3.13s Cat 2.67s 1.97s 3.56s Man 2.49s 4.45s Table 6.3 The computational results for the CGTV, CPA, SpB and PDHG algorithms.
It is known that the main computational steps of BOS (or SBB) and AM are the splitting Bregman iteration, which are equivalent to ADMM and the PDHG iterations, respectively.
(2) Relation between FBOSP and PDHG. FBOSP based on the projection gradient method can be regarded as a PDHG technique without the proximal term in the gradient descent step, applied to the primal-dual formulation:
The PDHG method cannot obtain accurate segmentation results.
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