Smoothing and Regularization with Modified Sparse Approximate Inverses

Table 5

Optimal reconstruction error ‖𝑝−𝑝‖̃₂ at given iteration for the blur problem of [24] invoked with blur(150,4,1) for noise of order 0.01%, 0.1%, 1%, and 10%. Subspace weight is 𝜌=1.

Regularization method	Noise level 0.01%		Noise level 0.1%
	‖𝑝−𝑝‖̃2	at it.	‖𝑝−𝑝‖̃2	at it.
CG(𝐺)	25.637	3	41.828	1
CG(𝐺^𝑇𝐺)	24.123	19	37.807	2
PCG(𝐺), MSPAI with 𝑅5𝐺1,𝐺2,𝐺3	23.620	6	39.007	1
PCG(𝐺^𝑇𝐺), MSPAI with 𝑅5𝐺1,𝐺2,𝐺3	23.778	51	38.023	3
Regularization method	Noise level 1%		Noise level 10%
	‖𝑝−𝑝‖̃2	at it.	‖𝑝−𝑝‖̃2	at it.
CG(𝐺)	591.0	1	13.820⋅10^3	1
CG(𝐺^𝑇𝐺)	82.5	1	1.253⋅10^3	1
PCG(𝐺), MSPAI with 𝑅5𝐺1,𝐺2,𝐺3	189.8	1	4.104⋅10^3	1
PCG(𝐺^𝑇𝐺), MSPAI with 𝑅5𝐺1,𝐺2,𝐺3	69.7	1	0.962⋅10^3	1