Fast Multimodulus Blind Deconvolution Algorithms

A novel class of fast Multi-Modulus algorithms (fastMMA) for Blind Source Separation (BSS) and deconvolution are presented in this work. These are obtained through a fast fixed-point optimization rule used to minimize the Multi-Modulus (MM) criterion. Here, two BSS versions are provided to separate the sources either by finding the separation matrix at once or by separating a single source each time using a fast deflation technique. Further, the latter method is extended to cover systems of convolutive nature. Interestingly, these algorithms are implicitly shown to belong to the fixed step-size gradient descent family, henceforth, an algebraic variable step-size is proposed to make these algorithms converge even much faster. Apart from being computationally and performance-wise attractive, the new algorithms are free of any user-defined parameters.