Multidimensional signal processing using lower-rank tensor approximation

The paper presents a new fast optimal lower rank tensor approximation (FOLRTA) method for lower rank-(R₁,..., R_N) tensor approximation applied to multidimensional signal processing. It is founded on a new approach which consists of considering multidimensional data as global tensors instead of splitting them into matrices or vectors for later classical second order array processing. Its basic principle is to project the initial data tensor into the signal subspace, in each consecutive mode. The developed method is the first analytical solution to the Tucker3 tensor decomposition. We show in a simple example of noise reduction of a color image the efficiency of this method. It can also be applied in seismic, acoustics or multimedia signal processing.