  Channeled spectropolarimetry measures the spectrally resolved Stokes
parameters. A key aspect of this technique is to accurately reconstruct the
Stokes parameters from a modulated measurement of the channeled
spectropolarimeter. The state-of-the-art reconstruction algorithm uses the
Fourier transform to extract the Stokes parameters from channels in the Fourier
domain. While this approach is straightforward, it can be sensitive to noise
and channel cross-talk, and it imposes bandwidth limitations that cut off high
frequency details. To overcome these drawbacks, we present a reconstruction
method called compressed channeled spectropolarimetry. In our proposed
framework, reconstruction in channeled spectropolarimetry is an underdetermined
problem, where we take N measurements and solve for 3N unknown Stokes
parameters. We formulate an optimization problem by creating a mathematical
model of the channeled spectropolarimeter with inspiration from compressed
sensing. We show that our approach offers greater noise robustness and
reconstruction accuracy compared with the Fourier transform technique in
simulations and experimental measurements. By demonstrating more accurate
reconstructions, we push performance to the native resolution of the sensor,
allowing more information to be recovered from a single measurement of a
channeled spectropolarimeter.
