A PCA-based automated finder for galaxy-scale strong lenses
  We present an algorithm using Principal Component Analysis (PCA) to subtract
galaxies from imaging data, and also two algorithms to find strong,
galaxy-scale gravitational lenses in the resulting residual image. The combined
method is optimized to find full or partial Einstein rings. Starting from a
pre-selection of potential massive galaxies, we first perform a PCA to build a
set of basis vectors. The galaxy images are reconstructed using the PCA basis
and subtracted from the data. We then filter the residual image with two
different methods. The first uses a curvelet (curved wavelets) filter of the
residual images to enhance any curved/ring feature. The resulting image is
transformed in polar coordinates, centered on the lens galaxy center. In these
coordinates, a ring is turned into a line, allowing us to detect very faint
rings by taking advantage of the integrated signal-to-noise in the ring (a line
in polar coordinates). The second way of analysing the PCA-subtracted images
identifies structures in the residual images and assesses whether they are
lensed images according to their orientation, multiplicity and elongation. We
apply the two methods to a sample of simulated Einstein rings, as they would be
observed with the ESA Euclid satellite in the VIS band. The polar coordinates
transform allows us to reach a completeness of 90% and a purity of 86%, as soon
as the signal-to-noise integrated in the ring is higher than 30, and almost
independent of the size of the Einstein ring. Finally, we show with real data
that our PCA-based galaxy subtraction scheme performs better than traditional
subtraction based on model fitting to the data. Our algorithm can be developed
and improved further using machine learning and dictionary learning methods,
which would extend the capabilities of the method to more complex and diverse
galaxy shapes.
