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Table 1 The normalized errors and runtimes of the DBIM and DCS-DBIM methods through iterations with different N t and N r

From: Deterministic compressive sampling for high-quality image reconstruction of ultrasound tomography

Number of Transmitters (N t ) and Receivers (N r ) Methods Normalized error from the first iteration to the eighth iteration Runtime (seconds)
N t  = N r  = 6 DBIM 0.8682 0.8438 NaN NaN NaN NaN NaN NaN 69.692787
(r = 0.082) DCS-DBIM 1.2077 1.2102 1.2105 1.2105 1.2105 1.2105 1.2105 1.2105 42.139530
N t  = N r  = 8 DBIM 0.7964 0.7515 0.7490 0.7489 0.7489 NaN NaN NaN 61.308944
(r = 0.145) DCS-DBIM 1.1587 1.1718 1.1721 1.1721 1.1721 1.1721 1.1721 1.1721 47.157182
N t  = N r  = 10 DBIM 0.7305 0.6811 0.6779 0.6772 0.6771 0.6770 0.6770 0.6770 40.428921
(r = 0.227) DCS-DBIM 1.1123 1.1224 1.1226 1.1226 1.1226 1.1226 1.1226 1.1226 53.017146
N t  = N r  = 12 DBIM 0.6808 0.6140 0.6083 0.6073 0.6070 0.6069 0.6069 0.6069 48.419012
(r = 0.327) DCS-DBIM 0.8834 0.8945 0.8950 0.8950 0.8950 0.8950 0.8950 0.8950 63.057426
N t  = N r  = 14 DBIM 0.9367 0.6457 0.5824 0.5547 0.5398 0.5308 0.5254 0.5218 55.754608
(r = 0.444) DCS-DBIM 0.7025 0.7084 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 90.422976
N t  = N r  = 16 DBIM 0.5272 0.4629 0.4585 0.4576 0.4572 0.4570 0.4570 0.4570 66.137258
(r = 0.581) DCS-DBIM 0.1604 0.1078 0.1082 0.1082 0.1082 0.1082 0.1082 0.1082 185.779095
N t  = N r  = 18 DBIM 0.8196 0.5734 0.4919 0.4480 0.4176 0.3948 0.3773 0.3632 77.524221
(r = 0.735) DCS-DBIM 0.1240 0.0342 0.0338 0.0337 0.0337 0.0337 0.0337 0.0337 251.473327
N t  = N r  = 20 DBIM 0.4749 0.2760 0.2356 0.2225 0.2158 0.2115 0.2086 0.2066 94.343578
(r = 0.907) DCS-DBIM 0.2243 0.0689 0.0672 0.0670 0.0670 0.0669 0.0668 0.0668 237.118941
N t  = N r  = 22 DBIM 0.4604 0.2106 0.1598 0.1353 0.1209 0.1110 0.1036 0.0973 112.128716
(r = 1.098) DCS-DBIM 0.3255 0.0777 0.0729 0.0724 0.0723 0.0721 0.0719 0.0718 234.584982
N t  = N r  = 24 DBIM 0.5754 0.2832 0.1321 0.0942 0.0725 0.0641 0.0534 0.0632 125.724742
(r = 1.306) DCS-DBIM 0.3870 0.0310 0.0197 0.0192 0.0190 0.0188 0.0186 0.0184 225.159681
N t  = N r  = 26 DBIM 0.5545 0.1933 0.1141 0.0846 0.0685 0.0585 0.0516 0.0464 144.661175
(r = 1.533) DCS-DBIM 0.1768 0.0129 0.0066 0.0064 0.0064 0.0064 0.0064 0.0064 201.250795
N t  = N r  = 28 DBIM 0.4905 0.1680 0.0858 0.0570 0.0417 0.0329 0.0271 0.0229 170.032561
(r = 1.778) DCS-DBIM 0.1338 0.0080 0.0031 0.0030 0.0029 0.0029 0.0029 0.0029 238.488285
N t  = N r  = 30 DBIM 0.5971 0.3079 0.2179 0.1602 0.1215 0.0948 0.0764 0.0633 212.923908
(r = 2.041) DCS-DBIM 0.1466 0.0062 0.0022 0.0022 0.0022 0.0022 0.0022 0.0022 263.288455