Table 4.2:

Quantitative results for the 1D constant coefficients test-case using the two-norm regularized solver (L₂) and the compressive sampling (CS) solver. The ground truth forward solver parameters are indicated by ‘ ^★’ and their respective reconstructed coefficient values by ‘rec’. We use a spatial discretization of 2π/256 with 256 grid points and a time discretization of 0.01 with 100 time steps. We consider the ground truth for the model constants as ρ^★ = 10, κ^★ = 0.05 to ensure a large tumor (larger tumors correspond to larger time horizons which make inverting for initial conditions hard). We report the relative error in inverted coefficient values (e_κ, e_ρ), the relative error in final tumor reconstruction (μ_T,L2), the relative error in the reconstructed initial condition (μ_0,L2), the relative error in the parameterization of the initial condition (μ_{p,$\mathcal{l}$1}), the relative change in the gradient (∥g∥rel) and solver timings (T_inv) in seconds.

Test case	Solver	k*	p*	Krec	eK	prec	eP	μT,L2	μ0,L2	μp,<1	||g||rel	Tinv [s]
1D-C1	L2	5E-2	1E1	1.03E-2	7.95E-1	1.05E0	8.69E-1	1.22E-3	3.95E0	1.43E1	6.69E-4	7.02E0
	CS	5E-2	1E1	4.76E-2	4.77E-2	9.41E0	5.89E-2	1.91E-4	6.49E-1	2.10E0	3.14E-6	9.05E0
1D-C2	L2	5E-2	1E1	1.71E-2	6.58E-1	1.20E0	8.50E-1	1.57E-3	3.84E0	1.19E1	4.34E-5	8.13E0
	CS	5E-2	1E1	5.07E-2	1.33E-2	1.09E1	9.41E-2	5.09E-2	8.80E-1	1.64E0	2.94E-6	1.17E1