A Fixed-Time Projection Neural Network for Solving L₁-Minimization Problem

In this article, a new projection neural network (PNN) for solving L₁ -minimization problem is proposed, which is based on classic PNN and sliding mode control technique. Furthermore, the proposed network can be used to make sparse signal reconstruction and image reconstruction. First, a sign function is introduced into the PNN model to design fixed-time PNN (FPNN). Then, under the condition that the projection matrix satisfies the restricted isometry property (RIP), the stability and fixed-time convergence of the proposed FPNN are proved by the Lyapunov method. Finally, based on the experimental results of signal simulation and image reconstruction, the proposed FPNN shows the effectiveness and superiority compared with that of the existing PNNs.

Paradigm free mapping with sparse regression automatically detects single-trial functional magnetic resonance imaging blood oxygenation level dependent responses

The ability to detect single trial responses in functional magnetic resonance imaging (fMRI) studies is essential, particularly if investigating learning or adaptation processes or unpredictable events. We recently introduced paradigm free mapping (PFM), an analysis method that detects single trial blood oxygenation level dependent (BOLD) responses without specifying prior information on the timing of the events. PFM is based on the deconvolution of the fMRI signal using a linear hemodynamic convolution model. Our previous PFM method (Caballero-Gaudes et al., 2011: Hum Brain Mapp) used the ridge regression estimator for signal deconvolution and required a baseline signal period for statistical inference. In this work, we investigate the application of sparse regression techniques in PFM. In particular, a novel PFM approach is developed using the Dantzig selector estimator, solved via an efficient homotopy procedure, along with statistical model selection criteria. Simulation results demonstrated that, using the Bayesian information criterion to select the regularization parameter, this method obtains high detection rates of the BOLD responses, comparable with a model-based analysis, but requiring no information on the timing of the events and being robust against hemodynamic response function variability. The practical operation of this sparse PFM method was assessed with single-trial fMRI data acquired at 7T, where it automatically detected all task-related events, and was an improvement on our previous PFM method, as it does not require the definition of a baseline state and amplitude thresholding and does not compromise on specificity and sensitivity.