Ht-index for empirical evaluation of the sampled graph-based Discrete Pulse Transform

The Discrete Pulse Transform decomposes a signal into pulses, with the most recent and effective implementation being a graph-base algorithm called the Roadmaker’s Pavage. Even though an efficient implementation, the theoretical structure results in a slow, deterministic algorithm. This paper examines the use of the spectral domain of graphs and designs graph filter banks to downsample the algorithm, investigating the extent to which this speeds up the algorithm. Converting graph signals to the spectral domain is costly, thus estimation for filter banks is examined, as well as the design of a reusable filter bank. The sampled version requires hyperparameters to reconstruct the same textures of the image as the original algorithm, preventing a large scale study. Here an objective and efficient way of deriving similar results between the original and our proposed Filtered Roadmaker’s Pavage is provided. The method makes use of the Ht-index, separating the distribution of information at scale intervals. Empirical research using benchmark datasets provides improved results, showing that using the proposed algorithm consistently runs faster, uses less computational resources, while having a positive SSIM with low variance. This provides an informative and faster approximation to the nonlinear DPT, a property not standardly achievable.