On the Uniqueness and Stability of Dictionaries for Sparse Representation of Noisy Signals

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

On the Uniqueness and Stability of Dictionaries for Sparse Representation of Noisy Signals

By: 
Charles J. Garfinkle; Christopher J. Hillar

Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very general conditions guaranteeing when dictionaries yielding the sparsest encodings are unique and stable with respect to measurement or modeling error. We demonstrate that some or all original dictionary elements are recoverable from noisy data even if the dictionary fails to satisfy the spark condition, its size is overestimated, or only a polynomial number of distinct sparse supports appear in the data. Importantly, we derive these guarantees without requiring any constraints on the recovered dictionary beyond a natural upper bound on its size. Our results yield an effective procedure sufficient to affirm if a proposed solution to the dictionary learning problem is unique within bounds commensurate with the noise. We suggest applications to data analysis, engineering, and neuroscience and close with some remaining challenges left open by our work.

SPS on Twitter

SPS Videos


Signal Processing in Home Assistants

 


Multimedia Forensics


Careers in Signal Processing             

 


Under the Radar