Sparse non-linear denoising: Generalization performance and pattern reproducibility in functional MRI

We investigate sparse non-linear denoising of functional brain images by kernel Principal Component Analysis (kernel PCA). The main challenge is the mapping of denoised feature space points back into input space, also referred to as ”the pre-image problem”. Since the feature space mapping is typically not bijective, pre-image estimation is inherently illposed.

In many applications, including functional magnetic resonance imaging (fMRI) data which is the application used for illustration in the present work, it is of interest to denoise a sparse signal. To meet this objective we investigate sparse pre-image reconstruction by Lasso regularization. We find that sparse estimation provides better brain state decoding accuracy and a more reproducible pre-image.

These two important metrics are combined in an evaluation framework which allow us to optimize both the degree of sparsity and the non-linearity of the kernel embedding. The latter result provides evidence of signal manifold non-linearity in the specific fMRI case study.