Hello, and welcome to the Paper of the Day (Po’D): Dynamic Iterative Pursuit. Today’s paper is D. Zachariah, S. Chatterjee and M. Jansson, “Dynamic Iterative Pursuit,” IEEE Trans. Signal Process., vol. 60, no. 9, pp. 4967-4972, Sep. 2012.
My one-line summary of this work is:
Do not compressively sample each frame of a dynamic signal as if it is unrelated to the previous frames.
The paper proposes some interesting new directions in the recovery of compressively sampled sparse dynamic signals using greedy pursuits. Consider each frame of some film transformed in some way that each is sparse. If the film is of some continuous process, then the transformations will likely exhibit continuity as well, with little change from frame to frame. Then, why not use that information to imbue the recovered frames with continuity? For instance, if transitions are slow, then a pixel that is detected as on in one frame will likely be on in the next frame. That is essentially what the “dynamic iterative pursuit” (DIP) does.
With modeling each support element as a first order AR process (with known decay weight and transition probabilities) with a zero-mean Gaussian innovation signal of known covariance, the authors pose orthogonal matching pursuit in a predictive framework (PrOMP, not to be confused with probabilistic OMP). The results look fantastic as the noise increases, but I must spend much more time in the details to understand what is going on — and this is a good opportunity to revisit my Kalman filtering notes from a long time ago!