  Coded Aperture Imaging (CAI) has been proposed as an alternative collimation
technique in nuclear imaging. To maximize spatial resolution small pinholes in
the coded aperture mask are required. However, a high-resolution detector is
needed to correctly sample the point spread function (PSF) to keep the
Nyquist-Shannon sampling theorem satisfied. The disadvantage of smaller pixels,
though, is the resulting higher Poisson noise. Thus, the aim of this paper was
to investigate if sufficiently accurate CAI reconstruction is achievable with a
detector which undersamples the PSF. With the Monte Carlo simulation framework
TOPAS a test image with multiple spheres of different diameter was simulated
based on the setup of an experimental gamma camera from previous work.
Additionally, measured phantom data were acquired. The captured detector images
were converted to low-resolution images of different pixel sizes according to
the super-resolution factor $k$. Multiple analytical reconstruction methods and
a Machine Learning approach were compared based on the contrast-to-noise ratio
(CNR). We show, that all reconstruction methods are able to reconstruct both
the test image and the measured phantom data for $k \leq 7$. With a synthetic
high-resolution PSF and upsampling the simulated low-resolution detector image
by bilinear interpolation the CNR can be kept approximately constant. Results
of this simulation study and additional validation on measured phantom data
indicate that an undersampling detector can be combined with small aperture
holes. However, further experiments need to be conducted.
