  Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable
recovery performance, surpassing traditional linear methods. However, unlike
traditional ID approaches that rely on analytical properties of the point
spread function (PSF) to achieve high recovery performance - such as specific
spectrum properties or small conditional numbers in the convolution matrix - DL
techniques lack quantifiable metrics for evaluating PSF suitability for
DL-assisted recovery. Aiming to enhance deconvolution quality, we propose a
metric that employs a non-linear approach to learn the invertibility of an
arbitrary PSF using a neural network by mapping it to a unit impulse. A lower
discrepancy between the mapped PSF and a unit impulse indicates a higher
likelihood of successful inversion by a DL network. Our findings reveal that
this metric correlates with high recovery performance in DL and traditional
methods, thereby serving as an effective regularizer in deconvolution tasks.
This approach reduces the computational complexity over conventional condition
number assessments and is a differentiable process. These useful properties
allow its application in designing diffractive optical elements through
end-to-end (E2E) optimization, achieving invertible PSFs, and outperforming the
E2E baseline framework.
