A parallel subgradient projections method for the convex feasibility problem
Journal of Computational and Applied Mathematics
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
SIAM Journal on Optimization
Sensor selection via convex optimization
IEEE Transactions on Signal Processing
Fundamentals of Computerized Tomography: Image Reconstruction from Projections
Fundamentals of Computerized Tomography: Image Reconstruction from Projections
IEEE Transactions on Signal Processing
Computational Optimization and Applications
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Sensor selection via compressed sensing
Automatica (Journal of IFAC)
Hi-index | 7.29 |
A computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS), is presented. The theory of CS usually leads to a constrained convex minimization problem. In this work, an alternative outlook is proposed. Instead of solving the CS problem as an optimization problem, it is suggested to transform the optimization problem into a convex feasibility problem (CFP), and solve it using feasibility-seeking sequential and simultaneous subgradient projection methods, which are iterative, fast, robust and convergent schemes for solving CFPs. As opposed to some of the commonly-used CS algorithms, such as Bayesian CS and Gradient Projections for sparse reconstruction, which become inefficient as the problem dimension and sparseness degree increase, the proposed methods exhibit robustness with respect to these parameters. Moreover, it is shown that the CFP-based projection methods are superior to some of the state-of-the-art methods in recovering the signal's support. Numerical experiments show that the CFP-based projection methods are viable for solving large-scale CS problems with compressible signals.