Natural images follow statistics inherited by the structure of our physical (visual) environment. In particular, a prominent facet of this structure is that images can be described by a relatively sparse number of features. Strikingly, this sparseness has a strong spatial component such that in general some sub-parts of an image are uniform while others contain clusters of textural (dense) structures. To investigate the role of this facet of images' sparseness in the efficiency of the neural code, we designed a new class of random textured stimuli with a controlled parameter inspired by measurements made on a dataset of natural images. Then, we tested the impact of this parameter on the firing pattern observed in a population of retinal ganglion cells recorded ex vivo in the retina of a diurnal rodent. These recordings showed in particular that the reliability of spike timings co-varied with respect to the spatial sparseness with a similar trend than that observed in natural images. These results suggest that the code represented in the spike pattern of ganglion cells may adapt to this aspect of the statistics of natural images.