Sparse modelling with the lp norm of 0 ≤ p ≤ 1 requires the availability of the proximity operator of the lp norm. The proximity operators of the l0 and l1 norms are the well-known hard- and soft-thresholding estimators, respectively. In this study, the authors give a complete study on the properties of the proximity operator of the lp norm. Based on these properties, explicit formulas of the proximity operators of the l1/2 norm and l2/3 norm are derived with simple proofs; for other values of p, an iterative Newton's method is developed to compute the proximity operator of the lp norm by fully exploring the available proximity operators of the l0, l1/2, l2/3, and l1 norms. As applications, the proximity operator of the lp norm with 0 ≤ p ≤ 1 is applied to the lp-regularisation for compressive sensing and image restoration.
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering