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When a line graph is symmetric, the associated graph Fourier transform has a fast implementation. In this paper, we extend this idea to the 2D non-separable case, where the graph of interest is a square-shaped grid. We investigate a number of symmetry types for 2D grids. Then, for each type of symmetry we derive a block-diagonalization form of the graph Laplacian matrix, based on which fast implementations...
In this paper, we study graph-based transforms for inter predictive video coding. We are motivated by the fact that symmetries in the transform basis are very beneficial for computational efficiency. Based on this, we describe the relationship between bisymmetric matrices and the butterfly structure in fast transform algorithms. We introduce a new class of transforms called Symmetric Line Graph Transforms...
In this letter we focus on discrete integer-periodic signals, whose periodicity are different from the periodicity of continuous periodic signals in many aspects. We introduce a class of discrete periodic signals called intrinsic integer-periodic function (IIPF). An IIPF contains only a single period in terms of downsampling, which leads to some interesting properties for analyzing periodic components...
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