A Wavelet-Based Multiresolution Reconstruction Method for Fluorescent Molecular Tomography

Algorithm 1

(1) Calculate 𝐀_𝑥 and 𝐒_𝑥 according to (10) and (11);

(2) For 𝑙=−1,…,−𝐿, perform wavelet transform of 𝐀_𝑥

    and 𝐒_𝑥 to obtain 𝐀_𝑥,𝑙 and 𝐒_𝑥,𝑙;

(3) Set 𝑙=−𝐿 and Φ⁽⁰⁾_𝑥,−𝐿=0;

(4) While (𝑙<0)

   {

 Solve 𝐀_𝑥,𝑙Φ_𝑥,𝑙=𝐒_𝑥,𝑙 with the conjugate gradient descent

 (CGD) method with an initial value of Φ⁽⁰⁾_𝑥,𝑙;

 Prolongate Φ_𝑥,𝑙 through padding zeros to obtain an initial

 guess for Φ_𝑥,𝑙+1 at the (𝑙+1)th level, that is,

  Φ⁽⁰⁾_𝑥,𝑙+1=[Φ^𝑇_𝑥,𝑙,𝟎^𝑇]^𝑇;

 Let 𝑙=𝑙+1;

   }

(5) Solve 𝐀_𝑥Φ_𝑥=𝐒_𝑥 with Φ_𝑥⁽⁰⁾=𝐖^T_Φ,0Φ⁽⁰⁾_𝑥,0 as an initial guess.