Dictionary Learning Strategies for Compressed Fiber Sensing Using a Probabilistic Sparse Model
This work addresses compressed fiber sensing for applications like structural health monitoring, presenting an incremental advancement in handling dictionary coherence through novel probabilistic models.
The paper tackles the problem of compressed fiber sensing by developing a sparse estimation and dictionary learning framework using a probabilistic hierarchical sparse model, achieving selective and collective shrinkage to handle dictionary coherence. The method's performance is evaluated through simulations and experimental data, showing improvements over existing methods in various scenarios.
We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior, which can be related to non-convex optimization with $p$-norm constraints for $0 < p < 1$. In addition, we leverage the specific dictionary structure to promote collective shrinkage based on a local similarity model. This is incorporated in form of a kernel function in the joint prior density of the sparse coefficients, thereby establishing a Markov random field-relation. Approximate inference is accomplished using a hybrid technique that combines Hamilton Monte Carlo and Gibbs sampling. To estimate the dictionary parameter, we pursue two strategies, relying on either a deterministic or a probabilistic model for the dictionary parameter. In the first strategy, the parameter is estimated based on alternating estimation. In the second strategy, it is jointly estimated along with the sparse coefficients. The performance is evaluated in comparison to an existing method in various scenarios using simulations and experimental data.