Block 2-D interpolation, efficient matrix factorization and application to signal processing

A block 2-D decomposition and a new block LU matrix factorization based on a Newton approach are presented for solving quickly and efficiently polynomial or exponential 2-D interpolation problems. The sample grids under consideration are described by the product representation {x₀, x₁, . . ., x_n} x{y₀, y ₁, . . ., y_m}, where the x grid and the y-grid are not necessarily uniformly spaced. The attractive features of the method are the inherent efficient parallelism, the reduced computational requirements needed for the LU decomposition, and the capability of implementation of 1-D fast and accurate algorithms. The proposed method can be used for modeling 2-D discrete signals, designing 2-D FIR filters, 2-D Fourier matrix factorization, 2-D DFT, etc