  Recently, non-regular three-quarter sampling has shown to deliver an
increased image quality of image sensors by using differently oriented L-shaped
pixels compared to the same number of square pixels. A three-quarter sampling
sensor can be understood as a conventional low-resolution sensor where one
quadrant of each square pixel is opaque. Subsequent to the measurement, the
data can be reconstructed on a regular grid with twice the resolution in both
spatial dimensions using an appropriate reconstruction algorithm. For this
reconstruction, local joint sparse deconvolution and extrapolation (L-JSDE) has
shown to perform very well. As a disadvantage, L-JSDE requires long computation
times of several dozen minutes per megapixel. In this paper, we propose a
faster version of L-JSDE called recurrent L-JSDE (RL-JSDE) which is a
reformulation of L-JSDE. For reasonable recurrent measurement patterns, RL-JSDE
provides significant speedups on both CPU and GPU without sacrificing image
quality. Compared to L-JSDE, 20-fold and 733-fold speedups are achieved on CPU
and GPU, respectively.
