The fundamental assumption in retinex is that the observed image is a multiplication between the illumination and the true underlying reflectance of the object.
We define our retinex model in two steps: First, we look for a filtered gradient that is the solution of an optimization problem consisting of two terms: A sparsity prior of the reflectance, such as the TV or H1 norm, and a quadratic fidelity prior of the reflectance gradient with respect to the observed image gradients.

In a second step, since this filtered gradient almost certainly is not a consistent image gradient, we then look for a reflectance whose actual gradient comes close.

Beyond unifying existing models, we are able to derive entirely novel retinex formulations by using more interesting non-local versions for the sparsity and fidelity prior. Hence we define within a single framework new retinex instances particularly suited for texture-preserving shadow removal, cartoon-texture decomposition, color and hyperspectral image enhancement.

When using this code, please do cite our underlying papers:

D. Zosso, G. Tran, S. Osher, "A unifying retinex model based on non-local differential operators," IS&T / SPIE Electronic Imaging: Computational
Imaging XI, San Francisco, USA, 2013.
DOI: http://dx.doi.org/10.1117/12.2008839
Preprint: ftp://ftp.math.ucla.edu/pub/camreport/cam13-03.pdf

D. Zosso, G. Tran, S. Osher, "Non-local Retinex - A Unifying Framework and Beyond," SIAM Journal on Imaging Science (submitted).
Preprint: ftp://ftp.math.ucla.edu/pub/camreport/cam14-49.pdf