Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration

For parts (a)–(c), the candidate solution’s closed-form ADMM updates for v (s=1 clamped shrinkage; s=2 normal equations) and the FFT-diagonalizable w-update exactly match the paper’s stated formulas and algorithmic setup (Eqs. (3)–(6)), including the z-hat clamping rule and the Fourier symbol of Δ^n . The paper asserts diffeomorphism via compositions of sufficiently small, smooth velocity fields (a standard claim) but does not supply a precise hypothesis or proof beyond citing prior topological results and showing empirical det(Jφ)≥0; the candidate supplies a rigorous sufficient condition ||∇v_i||∞<1 with a constructive proof via the inverse function theorem and contraction mapping, thereby strengthening the paper’s informal justification . Net: both are correct; the candidate gives fuller mathematical details for (d).