Design of three‐dimensional digital filters based on the outer product expansion of impulse response specifications

In dynamic image processing, medical image processing and seismic signal processing, high‐level processing, which cannot be executed by 1‐D or 2‐D signal processing, is expected to be realized by 3‐D digial signal processing. This paper proposed an efficient design method of 3‐D digital filters by the 3‐D outer product expansion which was proposed to decompose 3‐D arrays in image coding. In the proposed method, the given specification for the 3‐D filter is decomposed into the specifications for 1‐D filters using 3‐D outer product expansion and reducing the design of the 3‐D filter to that of the 1‐D filters. When the given impulse response specification is symmetrical, the computation required for the design in the proposed method can be reduced.