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Original Articles

A regularized solution for the inverse conductivity problem using mollifiers

, &
Pages 145-161 | Received 15 Oct 2008, Accepted 15 Feb 2009, Published online: 28 Sep 2009

Figures & data

Figure 1. (a) The conductivity distribution σ1(x, y); the reconstructed conductivity, , for data with 1% errors: (b) j(θ) = cos(θ), ; (c) j(θ) = cos(2θ), ; (d) j(θ) = sin(θ), .

Figure 1. (a) The conductivity distribution σ1(x, y); the reconstructed conductivity, , for data with 1% errors: (b) j(θ) = cos(θ), ; (c) j(θ) = cos(2θ), ; (d) j(θ) = sin(θ), .

Figure 2. (a) The conductivity distribution σ2(x, y); the reconstructed conductivity, , for data with 1% errors: (b) j(θ) = cos(θ), ; (c) j(θ) = cos(2θ), ; (d) j(θ) = sin(θ), .

Figure 2. (a) The conductivity distribution σ2(x, y); the reconstructed conductivity, , for data with 1% errors: (b) j(θ) = cos(θ), ; (c) j(θ) = cos(2θ), ; (d) j(θ) = sin(θ), .

Figure 3. (a) The conductivity distribution σ3(x, y); the reconstructed conductivity, , for data with 1%: (b) j(θ) = cos(θ), ; (c) j(θ) = cos(2θ), ; (d) j(θ) = sin(θ), .

Figure 3. (a) The conductivity distribution σ3(x, y); the reconstructed conductivity, , for data with 1%: (b) j(θ) = cos(θ), ; (c) j(θ) = cos(2θ), ; (d) j(θ) = sin(θ), .

Figure 4. The L2-relative error, , as a function of noise level ε for the conductivity distribution considered in Example 8.2 and input current j(θ) = cos(θ).

Figure 4. The L2-relative error, , as a function of noise level ε for the conductivity distribution considered in Example 8.2 and input current j(θ) = cos(θ).

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