Sparse Representation of Complex-Valued fMRI Data Based on Hard Thresholding of Spatial Source Phase

Abstract

Spatial source phase (SSP), derived from complex-valued functional magnetic resonance imaging (fMRI) data by datadriven methods, has unique capacity of identifying blood oxygenation-level dependent (BOLD)-related voxels from noisy voxels regardless of their amplitudes. However, the use of SSP constraint in sparse representation algorithms have rarely been studied. This study proposes a sparse representation method using SSP hard thresholding to achieve the sparsity of spatial components, enabling the use of initially complex-valued fMRI data and retaining the brain information embedded in noisy voxels and weak BOLDrelated voxels with small phase values. Rank-1 matrix estimation is applied to sequentially update dictionary atoms and corresponding spatial components, followed by hard thresholding on spatial components based on SSP. The proposed method is evaluated using both simulated and experimental complex-valued data. The results show that the proposed method yields better performance than a complexvalued dictionary learning algorithm when using initially acquired complex-valued task-related fMRI data.

Denoising brain networks using a fixed mathematical phase change in independent component analysis of magnitude‐only fMRI data

“…Different from the meaningless phase changes for the random complex Gaussian noise, as shown in Figure 1 , smaller SSP phase changes (∆ φ ≤ π /4) correspond to BOLD‐related voxels, whereas larger SSP phase changes (∆ φ > π /4) are unwanted voxels (Lin et al, 2022 ; Yu et al, 2015 ), after removing the phase ambiguity of an ICA complex‐valued map. Based on this, a fixed phase change (∆ φ = π /4) has been used to generate a binary mask in the SSP denoising of ICA spatial maps for both task‐related and resting‐state fMRI data (Iqbal et al, 2020 ; Kuang et al, 2020 ; Kuang, Lin, Gong, Cong, et al, 2017a ; Lin et al, 2022 ; Qiu et al, 2019 ; Song et al, 2021 ). More desired voxels can remain when using a large phase change ∆ φ = π /4 than using a smaller one (∆ φ < π /4).…”