Combined Energy Minimization for Image Reconstruction from Few Views

Algorithm 1

Iteration algorithm for CL minimization reconstruction.

% Initialization

maxGrad = 10⁻³; maxIter = 100; maxTau = 10⁻³; 𝑠 = 4; 𝑘 = 0;

𝜏₀ = 1; 𝑔₀ = ∇𝜀_CCL(𝑓₀); Δ𝑓₀ = −𝑔₀;

% Iterations

while (‖𝑔_𝑘‖₂ > maxGrad and 𝑘 < maxIter and 𝜏 > maxTau){

  %Linear search

  min𝐸 = 𝜀_CCL(𝑓_𝑘); opt = 0; 𝑖 = −𝑠;

  while (𝑖 <= s){

    𝜏=2^−𝑖𝜏₀;

    if (𝜀_CCL(𝑓_𝑘 + 𝜏Δ𝑓_𝑘) < min𝐸){min𝐸 = 𝜀_CCL(𝑓_𝑘 + 𝜏Δ𝑓_𝑘); opt = 𝜏; }

    𝑖=𝑖+1; }

  𝜏₀ = opt;

  𝑓_𝑘+1 = 𝑓_𝑘+𝜏₀Δ𝑓_𝑘; 𝑔_𝑘+1 = ∇𝜀_CCL (𝑓_𝑘+1); 𝛾 = ‖𝑔_𝑘+1‖₂‖Δ𝑓_𝑘‖₂;

  Δ𝑓_𝑘+1 = −𝑔_𝑘+1 + 𝛾Δ𝑓_𝑘;

  𝑘 = 𝑘 + 1; }