2013/10/31 by Will Landecker, Landecker, Will, Rick Chartrand +3
Computer Science · Engineering · Medicine · #Blind Source Separation Techniques #Computer Vision and Pattern Recognition (cs.CV) #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (stat.ML) #Medical Imaging Techniques and Applications #Sparse and Compressive Sensing Techniques #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1311.0053
openalex publication_date 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In compressed sensing, we wish to reconstruct a sparse signal x from observed data y. In sparse coding, on the other hand, we wish to find a representation of an observed signal y as a sparse linear combination, with coefficients x, of elements from an overcomplete dictionary. While many algorithms are competitive at both problems when x is very sparse, it can be challenging to recover x when it is less sparse. We present the Difference Map, which excels at sparse recovery when sparseness is lower and noise is higher. The Difference Map out-performs the state of the art with reconstruction from random measurements and natural image reconstruction via sparse coding.