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Table 1 Numerical comparison of our method and the MM method for two kinds of BCs, ZBC, and PBC

From: New inexact explicit thresholding/shrinkage formulas for inverse problems with overlapping group sparsity

BC

β=

1

5

7

10

15

20

30

50

ZBC

\(\text {ReE}_{f_{A}}\)

5.9e-14

0.0055

0.0028

6.5e-4

1.4e-4

5.4e-5

1.4e-5

2.6e-6

 

ReE X

—

—

0.0207

0.0017

1.9e-4

4.7e-5

7.5e-6

7.8e-7

 

MAE X

3.4e-15

0.0094

0.0130

0.0067

0.0029

0.0016

6.9e-4

2.4e-4

PBC

\(\text {ReE}_{f_{A}}\)

6.5e-14

0.0053

0.0025

4.1e-4

5.5e-5

1.1e-5

6.3e-7

1.3e-6

 

ReE X

—

—

0.0193

0.0014

1.3e-4

2.9e-5

4.3e-6

4.5e-7

 

MAE X

3.8e-15

0.0097

0.0130

0.0063

0.0026

0.0014

5.9e-4

2.1e-4

  1. ReE of f A (X) denotes the related error of final function value fun (X). ReE of X denotes related error of minimizer X. MAE of X denotes the mean absolute error of X
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