Dictionary learning for L1-exact sparse coding

We have derived a new algorithm for dictionary learning for sparse coding in the E, exact sparse framework. The algorithm does not rely on an approximation residual to operate, but rather uses the special geometry of the l(1) exact sparse solution to give a computationally simple yet conceptually interesting algorithm. A self-normalizing version of the algorithm is also derived, which uses negative feedback to ensure that basis vectors converge to unit norm. The operation of the algorithm is illustrated on a simple numerical example.