The Discrete Orthonormal Stockwell Transform and Variations, with Applications to Image Compression

We examine the so-called Discrete Orthonormal Stockwell Transform (DOST) and show that a number of quite simple modifications can be made to obtain various desired properties. For example, we introduce a real-valued Discrete Cosine-based DOST (DCST). The coefficients of the DOST and its variations are shown to exhibit a directed graph structure as opposed to the tree-like structure demonstrated by wavelet coefficients. Finally, we employ the DOST and DCST in a series of simple compression experiments and compare the results to those obtained with biorthogonal wavelets and the DCT.