The first was done by Kavita Bala's group at Cornell University. Their approach, entitled "Feature-based textures" targets the exact same problems with texture magnification that we address.
Feature-based textures do this by embedding spline curves into the cells of their representation. They can have an arbitrary number of spline curves in each cell, and reconstruction involves tracing a ray between the point to be shaded and the color sample locations to determine if there are spline curves in the way or not. Color samples will not be used if there are spline curves in the way.
Since this approach involves 2-D ray-spline intersections and a potentially unbounded number of edges per cell, it might be difficult to implement it on graphics hardware so that it can run in real-time. Thus their approach mostly targets high-end offline applications.