Robust Sparse Component Analysis Based on a Generalized Hough Transform

An algorithm called Hough SCA is presented for recovering the matrix[inline-graphic not available: see fulltext] in[inline-graphic not available: see fulltext], where[inline-graphic not available: see fulltext] is a multivariate observed signal, possibly is of lower dimension than the unknown sources[inline-graphic not available: see fulltext]. They are assumed to be sparse in the sense that at every time instant[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext] has fewer nonzero elements than the dimension of[inline-graphic not available: see fulltext]. The presented algorithm performs a global search for hyperplane clusters within the mixture space by gathering possible hyperplane parameters within a Hough accumulator tensor. This renders the algorithm immune to the many local minima typically exhibited by the corresponding cost function. In contrast to previous approaches, Hough SCA is linear in the sample number and independent of the source dimension as well as robust against noise and outliers. Experiments demonstrate the flexibility of the proposed algorithm.