Truncated Total Least Squares Method with a Practical Truncation Parameter Choice Scheme for Bioluminescence Tomography Inverse Problem

Table 4

Quantitative results for ball shape permission region𝑃𝑅^′ in double source case.

Sys. error	Meas. noise	Recon. method	Regular. param.	RRE	Recon. position (mm) and power (nW)
					𝑆^𝑅1		𝑆^𝑅2
1%	10%	Tik-GCV	0.02728	0.1720	(−8.80,−3.62,15.00)	0.2102	(−8.32,2.81,16.44)	0.2509
		TTLS-M	19	0.1535	(−8.80,−3.62,15.00)	0.2308	(−8.77,3.88,14.85)	0.2373
		TTLS-I	30	0.1523	(−𝟖.𝟖𝟎,−𝟑.𝟔𝟐,𝟏𝟓.𝟎𝟎)	0.2978	(−𝟗.𝟒𝟐,𝟏.𝟔𝟗,𝟏𝟒.𝟗𝟒)	0.3062
	20%	Tik-GCV	0.09397	0.4383	(−10.27,−2.24,16.42)	0.3633	(−10.97,2.08,16.69)	0.3501
		TTLS-M	9	0.4288	(−8.80,−3.62,15.00)	0.3782	(−8.77,3.88,14.85)	0.3651
		TTLS-I	28	0.4226	(−𝟗.𝟐𝟎,−𝟏.𝟔𝟐,𝟏𝟒.𝟏𝟐)	0.5808	(−𝟖.𝟑𝟐,𝟐.𝟖𝟏,𝟏𝟔.𝟒𝟒)	0.4632
5%	10%	Tik-GCV	0.09660	0.2350	(−10.27,−2.24,16.42)	0.3693	(−8.77,3.88,14.85)	0.3784
		TTLS-M	9	0.2350	(−8.80,−3.62,15.00)	0.3752	(−8.77,3.88,14.85)	0.3853
		TTLS-I	18	0.2171	(−𝟖.𝟖𝟎,−𝟑.𝟔𝟐,𝟏𝟓.𝟎𝟎)	0.3899	(−𝟖.𝟑𝟐,𝟐.𝟖𝟏,𝟏𝟔.𝟒𝟒)	0.4234
	20%	Tik-GCV	0.12804	0.4367	(−10.27,−2.24,16.42)	0.3549	(−8.77,3.88,14.85)	0.3578
		TTLS-M	15	0.3865	(−8.80,−3.62,15.00)	0.3900	(−8.77,3.88,14.85)	0.3653
		TTLS-I	19	0.3532	(−𝟖.𝟖𝟎,−𝟑.𝟔𝟐,𝟏𝟓.𝟎𝟎)	0.4538	(−𝟖.𝟕𝟕,𝟑.𝟖𝟖,𝟏𝟒.𝟖𝟓)	0.3807