  Two different approaches have recently been proposed for boundary handling in
convolutional sparse representations, avoiding potential boundary artifacts
arising from the circular boundary conditions implied by the use of frequency
domain solution methods by introducing a spatial mask into the convolutional
sparse coding problem. In the present paper we show that, under certain
circumstances, these methods fail in their design goal of avoiding boundary
artifacts. The reasons for this failure are discussed, a solution is proposed,
and the practical implications are illustrated in an image deblurring problem.
