Algorithm 1.

Self-sparse NMR spectra reconstruction with undersampled data using PSOCA.

Initialization:

Input the sampled FID data y, set the regularization parameter λ =108 and tolerance of inner loop η = 5 × 10−3. Initialize x = FΘTy, xlast = x, β = 26, and α = 0.

Main:

Whileβ ≤ 216

Inner loop:

1. Given x,

Forj = 1 to J, solve Equation (20), the solution is α;

2. Given α,       solve Equation (22), the solution is x;

3. If ‖Δx‖ = ‖xlast – x‖ > η,xlast ← x, go to step 1;         Otherwise, go to step 4;

Outer loop:

4. x̂ ← x, β ← 2β, go to step 1.

End While

Output: x̂