Dimension-independent lower-isometry constant for coded diffraction patterns

Determine whether the logarithmic factors in the uniform lower-isometry bound for the lifted coded diffraction pattern measurement operator are intrinsic, or whether a dimension-independent lower-isometry constant can be obtained, thereby sharpening stable recovery guarantees and logarithmic scalings.

Background

The paper proves that, with an optimal-order number of masks L asymptotic to log n, the lifted coded diffraction pattern measurement operator satisfies a uniform lower-isometry inequality over the positive-semidefinite secant set, but the bound loses a factor of order log^4(n). This loss propagates to the stable recovery estimate, which has an error factor of order log^2(n) times the noise norm divided by the square root of nL.

The authors explicitly leave unresolved whether these logarithmic losses reflect genuine limitations of coded diffraction measurements or are artifacts of the proof techniques, particularly the row-subset estimates and dual-certificate construction. Removing them would yield a dimension-independent stability constant and sharper recovery guarantees.