Accurate Computation of Fractional-Order Exponential Moments

Table 9

GFrEMs amplitude and error data [41].

Attack										MRE
Original image	2.7269	4.5518	2.7743	3.1475	2.4092	1.8828	2.4346	1.4592	0.5893	0
Rotation	2.7302	4.5458	2.7697	3.1432	2.3974	1.8810	2.4241	1.4498	0.5873	0.0035
Rotation	2.7263	4.5496	2.7645	3.1476	2.4004	1.8807	2.4292	1.4519	0.5869	0.0034
Rotation	2.7154	4.5444	2.7546	3.1560	2.3968	1.8862	2.4357	1.4475	0.5939	0.0057
Rotation	2.7143	4.5466	2.7506	3.1639	2.4014	1.8903	2.4358	1.4433	0.5898	0.0061
Rotation	2.7232	4.5460	2.7411	3.1541	2.3963	1.8935	2.4342	1.4565	0.5984	0.0061
JPEG 90	2.7170	4.5359	2.7673	3.1415	2.4018	1.8745	2.4138	1.4466	0.5930	0.0054
JPEG 80	2.7111	4.5286	2.7568	3.1407	2.4027	1.8614	2.3984	1.4361	0.5933	0.0085
JPEG 70	2.7080	4.5053	2.7515	3.1499	2.4062	1.8828	2.3791	1.4580	0.5972	0.0080
JPEG 60	2.7115	4.5223	2.7450	3.1302	2.3968	1.8709	2.3609	1.4350	0.5910	0.0111
JPEG 50	2.6942	4.5107	2.7673	3.1265	2.3894	1.8607	2.3518	1.4157	0.5901	0.0162
JPEG 40	2.7024	4.5454	2.7428	3.1117	2.3790	1.8496	2.3502	1.4251	0.6031	0.0194
JPEG 30	2.6388	4.5037	2.7269	3.1086	2.3940	1.8565	2.3656	1.4065	0.5876	0.0160
JPEG 20	2.7084	4.4552	2.8115	3.0255	2.3861	1.8364	2.2966	1.3742	0.5975	0.0316
JPEG 10	2.5927	4.4060	2.7480	3.1508	2.3103	1.7518	2.3970	1.2439	0.5875	0.0378
Scaling 0.5	2.7377	4.6098	2.7222	3.0443	2.4141	1.9277	2.3103	1.5137	0.6864	0.0405
Scaling 0.75	2.7279	4.5653	2.7606	3.1183	2.3982	1.8971	2.3995	1.4640	0.6250	0.0147
Scaling 1.5	2.7224	4.5211	2.7663	3.1732	2.3820	1.8699	2.4440	1.4165	0.5607	0.0131
Scaling 2.0	2.7250	4.5064	2.7722	3.1869	2.3694	1.8581	2.4536	1.3977	0.5406	0.0184
Median filtering 3 × 3	2.9419	4.6767	2.8092	3.2498	2.5348	1.8274	2.5845	1.3654	0.4837	0.0575
Gaussian filtering 3 × 3	2.7266	4.5450	2.7663	3.1469	2.3941	1.8820	2.4249	1.4457	0.5893	0.0045
Average filtering 3 × 3	2.7265	4.5302	2.7481	3.1446	2.3622	1.8811	2.4033	1.4173	0.5903	0.0141