Skip to main content

Table 1 Average relative reconstruction error over 100 simulations, as a function of the order of the method and number of levels in the multiscale approaches

From: Multiscale higher-order TV operators for L1 regularization

SNR Order 1 Order 2 Order 3 Order 1.5 Order 2.5
mhotv Daub mhotv Daub mhotv Daub mhotv mhotv
2
1 level .1624 .1624 .2039 .1961 .2464 .2306 .1819 .2328
2 levels .1612 .1617 .1742 .1852 .2135 .2223 .1782 .2183
3 levels .1699 .1615 .1513 .1778 .1745 .2149 .1776 .1975
4 levels .2001 .1647 .1584 .1745 .1764 .2104 .2031 .2102
5
1 level .0864 .0864 .0971 .0914 .1293 .1090 .1025 .1287
2 levels .0858 .0857 .0761 .0838 .0946 .1004 .0987 .1172
3 levels .0926 .0864 .0668 .0805 .0766 .0982 .1016 .1133
4 levels .1100 .0894 .0742 .0801 .0828 .0981 .1186 .1276
10
1 level .0543 .0542 .0509 .0480 .0694 .0572 .0690 .0841
2 levels .0542 .0539 .0400 .0442 .0489 .0528 .0657 .0763
3 levels .0589 .0547 .0359 .0430 .0399 .0522 .0694 .0776
4 levels .0696 .0570 .0413 .0436 .0442 .0535 .0802 .0880
  1. The minimums for each SNR are emphasized in italics