Which is better? Vector-vector decomposition or array-array decomposition

This paper proposes a new method for designing variable 2-D digital filters with arbitrarily variable 2-D frequency responses. The design method simplifies the difficult variable filter design problem to the easier one that only requires constant 2-D filter design and multi-dimensional (M-D) polynomial fitting. It includes the following steps. (1). Construction of a complex M-D array by sampling the variable 2-D frequency response specification. (2). Decomposition of the constructed M-D array into the sum of products of 2-D complex arrays (matrices) and M-D real arrays. (3). Approximation of the 2-D complex arrays by using constant 2-D digital filters, and best fitting the M-D real arrays by using M-D polynomials. (4). Interconnection of the obtained constant 2-D filters and M-D polynomials to form a variable 2-D digital filter