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Sparse non-linear denoising of fMRI : Performance and pattern reproducibility

Non-linear embedding improves mental state decoding in fMRI. Here we investigate the possibility of non-linear denoising by kernel Principal Component Analysis (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 MRI data, it is of interest to find a sparse signal, hence we investigate sparse reconstruction by Lasso regularization. It is found that sparse estimation provides better predictability and a more reproducible pre-image. Using the combined prediction/reproducibility metric we may optimize the degree of sparsity and the non-linearity of the kernel embedding.