  We report on the initial results obtained with an image
convolution/deconvolution computer code that we developed and used to study the
image formation capabilities of the solar gravitational lens (SGL). Although
the SGL of a spherical Sun creates a greatly blurred image, knowledge of the
SGL's point-spread function (PSF) makes it possible to reconstruct the original
image and remove the blur by way of deconvolution. We discuss the deconvolution
process, which can be implemented either with direct matrix inversion or with
the Fourier quotient method. We observe that the process introduces a
``penalty'' in the form of a reduction in the signal-to-noise ratio (SNR) of a
recovered image, compared to the SNR at which the blurred image data is
collected. We estimate the magnitude of this penalty using an analytical
approach and confirm the results with a series of numerical simulations. We
find that the penalty is substantially reduced when the spacing between image
samples is large compared to the telescope aperture. The penalty can be further
reduced with suitable noise filtering, which can yield ${\cal O}(10)$ or better
improvement for low-quality imaging data. Our results confirm that it is
possible to use the SGL for imaging purposes. We offer insights on the data
collection and image processing strategies that could yield a detailed image of
an exoplanet within image data collection times that are consistent with the
duration of a realistic space mission.
