Octonion based signal representations attract the attention for multichannel signal representations due to their property of processing multiple channels in a holistic manner. This leads to better preservation of the correlation among different channels of a given signal. The aim of this talk is to provide an introduction to the mathematical theory of octonion signal processing, with special emphasis on theoretical and practical questions such as accuracy and performance guarantees of three different sparse coding methods for octonion valued signals. We explore a unified framework for formulating octonion sparse coding models in terms of the corresponding problems over real numbers, using thereby the efficient available solvers, and we compare the performance of $\ell_0$ and $\ell_1$ formulations under this setup.