First-Order Difference Energy Regularization for Enhancing Reconstruction Performance in Compressive Sensing of Foot-Gait Signals

A new method for the regularization of the objective function for the reconstruction of the foot-gait signal from compressively sensed measurements is proposed. The method is based on using the $\ell_{2}$ norm of the first-order difference to regularize the objective function. The state-of-the-art first-order difference sparsity promoting algorithms can introduce transient artefacts in the signal. The proposed regularization helps to reduce such artefacts. Involved optimization can be solved by using a sequential optimization procedure. The resulting algorithm is useful for enhancing the quality of reconstructed signal, especially in the situations when the CS system is applied with extremely high compression ratio. Simulation results indicate that the proposed method can offer upto 2.81dB improvement in signal-to-noise ratio, 0.02 units improvement in structural similarity measure, and a marginal increase in the computational effort.