A different recursive formulation of 2D digital inverse filter

A 1-D inverse (or deconvolution) filtering problem is generally formulated in terms of a lower triangular Toeplitz matrix. A different formulation of a 2D inverse (or deconvolution) filter is presented which obtains the infinite impulse response (IIR) coefficients of the deconvolution filter in a computationally elegant recursive manner without any preconstraint on the size of the output array of sample values. On interchanging the 2D input signal and the unit sample response of the degrading physical medium in the formulation, the method presented can be extended to the identification of a physical system or the propagation medium of the input signal as is usually required in seismic signal processing (2-D) and speech processing (1-D). An example is provided to deconvolve a first order 2D reverberator obtaining a closed-form solution