  Images acquired with a telescope are blurred and corrupted by noise. The
blurring is usually modeled by a convolution with the Point Spread Function and
the noise by Additive Gaussian Noise. Recovering the observed image is an
ill-posed inverse problem. Sparse deconvolution is well known to be an
efficient deconvolution technique, leading to optimized pixel Mean Square
Errors, but without any guarantee that the shapes of objects (e.g. galaxy
images) contained in the data will be preserved. In this paper, we introduce a
new shape constraint and exhibit its properties. By combining it with a
standard sparse regularization in the wavelet domain, we introduce the Shape
COnstraint REstoration algorithm (SCORE), which performs a standard sparse
deconvolution, while preserving galaxy shapes. We show through numerical
experiments that this new approach leads to a reduction of galaxy ellipticity
measurement errors by at least 44%.
