Filtering by Sparsely Connected Networks Under the Presence of Strong Additive Noise

A new approach to the problem of noise reduction in signals composed by superpositions of basis functions is proposed. The method is based on interpreting the components of signal models as nodes in a sparsely connected network of overlaps (scalar products). Every point in the data sample expresses an overlap. Networks of this kind, in which nodes carry information by means of vectors, define a knowledge network, a recently introduced concept in the field of statistical physics. Previous results on the statistical properties of knowledge networks are generalized to noise reduction and its shown that is possible to extract important hidden quantities. In particular, an algorithm capable to give estimates of the unknown number of degrees of freedom in signal models is constructed and tested