  We present a framework for the end-to-end optimization of metasurface imaging
systems that reconstruct targets using compressed sensing, a technique for
solving underdetermined imaging problems when the target object exhibits
sparsity (i.e. the object can be described by a small number of non-zero
values, but the positions of these values are unknown). We nest an iterative,
unapproximated compressed sensing reconstruction algorithm into our end-to-end
optimization pipeline, resulting in an interpretable, data-efficient method for
maximally leveraging metaoptics to exploit object sparsity. We apply our
framework to super-resolution imaging and high-resolution depth imaging with a
phase-change material. In both situations, our end-to-end framework
computationally discovers optimal metasurface structures for compressed sensing
recovery, automatically balancing a number of complicated design considerations
to select an imaging measurement matrix from a complex, physically constrained
manifold with millions ofdimensions. The optimized metasurface imaging systems
are robust to noise, significantly improving over random scattering surfaces
and approaching the ideal compressed sensing performance of a Gaussian matrix,
showing how a physical metasurface system can demonstrably approach the
mathematical limits of compressed sensing.
