  Our goal is to revisit rank order coding by proposing an original exact
decoding procedure for it. Rank order coding was proposed by Simon Thorpe et
al. who stated that the retina represents the visual stimulus by the order in
which its cells are activated. A classical rank order coder/decoder was then
designed on this basis [1]. Though, it appeared that the decoding procedure
employed yields reconstruction errors that limit the model Rate/Quality
performances when used as an image codec. The attempts made in the literature
to overcome this issue are time consuming and alter the coding procedure, or
are lacking mathematical support and feasibility for standard size images. Here
we solve this problem in an original fashion by using the frames theory, where
a frame of a vector space designates an extension for the notion of basis.
First, we prove that the analyzing filter bank considered is a frame, and then
we define the corresponding dual frame that is necessary for the exact image
reconstruction. Second, to deal with the problem of memory overhead, we design
a recursive out-of-core blockwise algorithm for the computation of this dual
frame. Our work provides a mathematical formalism for the retinal model under
study and defines a simple and exact reverse transform for it with up to 270 dB
of PSNR gain compared to [1]. Furthermore, the framework presented here can be
extended to several models of the visual cortical areas using redundant
representations.
