Equal Sampling Budgets Can Preserve Different Fine Structures in Sparse MRI Reconstruction

Abstract

This illustrative numerical study asks whether equal Fourier sampling budgets and exact acquired data consistency imply similar preservation of fine structure in accelerated MRI. Forty eight synthetic complex phantoms contain a fixed alternating bar region. Three sixteen row Cartesian masks are compared with zero filling and two prescribed Haar sparse reconstructions on sixty four pixel grids. Central sampling gives low global magnitude error but recovers little alternating contrast. A fixed spread mask with standard Haar shrinkage recovers mean contrast ratio 0.290 while central sampling gives 0.009, although its global error is slightly larger. Periodic sampling remains unchanged by the tested shrinkage procedure, exposing a symmetry limitation. Every final reconstruction has acquired residual below 3 × 10⁻¹⁶. A constructed nonzero missing frequency perturbation leaves central acquired data unchanged. The evidence concerns a single coil Fourier proxy and does not assess patients, clinical diagnosis or trained reconstruction networks.