Sparsity-fused Kalman filtering for reconstruction of dynamic sparse signals

This article focuses on the problem of reconstructing dynamic sparse signals from a series of noisy compressive sensing measurements using a Kalman Filter (KF). This problem arises in many applications, e.g., Magnetic Resonance Imaging (MRI), Wireless Sensor Networks (WSN) and video reconstruction. The conventional KF does not consider the sparsity structure presented in most practical signals and it is therefore inaccurate when being applied to sparse signal recovery. To deal with this issue, we derive a novel KF procedure which takes the sparsity model into consideration. Furthermore, an algorithm, namely Sparsity-fused KF, is proposed based upon it. The method of iterative soft thresholding is utilized to refine our sparsity model. The superiority of our method is demonstrated by synthetic data and the practical data gathered by a WSN.