Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis

Table 1

and values of the images in Figure 1 affected by different values of Gaussian noise and their corresponding iteration number for both functions.

		Noisy		WZ [4]			Proposed
	Patient30	0.005	23.4311	0.3426	33.3757	0.9114	30	33.8333	0.9372	13
0.010		20.6839	0.2432	31.3367	0.8766	41	31.5737	0.9145	21
0.015		19.1190	0.1960	30.1565	0.8521	48	30.2008	0.8980	24
0.020		17.9763	0.1660	29.0905	0.8298	56	29.0007	0.8825	26
0.100		12.0756	0.0596	22.6821	0.6535	117	21.8953	0.7389	56
Patient50	0.005	23.6686	0.4424	31.1185	0.8708	24	31.2934	0.8769	11
	0.010	20.7561	0.3278	29.0893	0.8186	35	29.1527	0.8258	19
	0.015	19.1313	0.2707	27.9137	0.7820	41	27.8981	0.7920	26
	0.020	17.9838	0.2334	27.0011	0.7508	47	26.9714	0.7625	27
	0.100	11.9985	0.0911	21.4469	0.5585	93	20.9674	0.5932	62
Patient55	0.005	24.0179	0.3867	31.3190	0.9021	26	31.4668	0.9258	19
	0.010	21.2303	0.2892	29.1310	0.8600	36	29.0997	0.8887	28
	0.015	19.5990	0.2403	27.6640	0.8221	44	27.5635	0.8561	35
	0.020	18.4292	0.2096	26.7717	0.7938	49	26.5468	0.8305	42
	0.100	12.2234	0.0882	20.6948	0.5642	98	20.1755	0.6237	99