The impulse responses of block shift-invariant systems and their use for demosaicing algorithms

Shift-invariant linear algorithms can be described completely by the algorithm's response to an impulse input. The so called impulse response can be used as filter kernels when the algorithm is equivalently implemented using convolution. This, however, is not true when the system is block-shift invariant, i.e. when invariance is only at repetitive locations. This paper describes a generalization of the impulse response for block shift-invariant systems. The proposed technique, takes any computer program which implements a linear block-shift-invariant algorithm, and produces its equivalent filter kernels. These kernels can then be applied efficiently by using convolution. This scheme can assist in finding the filter kernels of linear operations applied directly to mosaic images acquired by digital cameras. For example, using this approach any algorithmic description for the demosaicing problem, which is linear and block shift-invariant, can be translated into actual filter kernels that can be applied efficiently.