Two-dimensional convolution using number theoretic transforms without matrix transposition and without overlap

The necessity of sectioning a large picture to compute a 2 dimensional convolution has many drawbacks, one of which is the size of the optimal sections. Starting from this consideration, it is shown that, if the input image array is a 22u × 22u matrix, the convolution can be computed efficiently using a small length Fermat number transform and, if enough fast memory space is provided, without transposing the matrix or overlap sectioning the input array. The paper investigates the case of pictures represented by approximately 1000 × 1000 pixels.