Independent component analysis has been widely applied to brain imaging and genetic data analyses for its ability to identify interpretable latent sources. Nevertheless, leveraging source sparsity in a more granular way may further improve its ability to optimize the solution for certain data types. For this purpose, we propose a sparse infomax algorithm based on nonlinear Hoyer projection, leveraging both sparsity and statistical independence of latent sources. The proposed algorithm iteratively updates the unmixing matrix by infomax (for independence) and the sources by Hoyer projection (for sparsity), feeding the sparse sources back as input data for the next iteration. Consequently, sparseness propagates effectively through infomax iterations, producing sources with more desirable properties. Simulation results on both brain imaging and genetic data demonstrate that the proposed algorithm yields improved pattern recovery, particularly under low signal-to-noise ratio conditions, as well as improved sparseness compared to traditional infomax.