RECORD
Linearly Constrained Smoothing Group Sparsity Solvers in Off-grid Model
Signal Processing · Submitted 17 Mar 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The performance of accuracy and convergence for all the proposed methods are demonstrated in the numerical simulations.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid effect satisfies this situation, and can be formulated into a (non)convex optimization problem with linear inequalities constraints, which can be solved by the interior point method (using the CVX tools), but at a large computational cost. In this work, in order to design efficient algorithms, we consider various alternative formulations, such as unconstrained formulation, primal-dual formulation, or conic formulation to develop group-sparsity promoted solvers. First, the consensus alternating direction method of multipliers (C-ADMM) is applied. Then, iterative algorithms for the BPDN formulation is proposed by combining the Nesterov smoothing technique with accelerated proximal gradient method, and the convergence analysis of the method is conducted as well. We also developed a variant of EGT (Excessive Gap Technique)-based primal-dual method to systematically reduce the smoothing parameter sequentially. Finally, we propose algorithms for quadratically constrained L2-L1 mixed norm minimization problem by using the smoothed dual conic optimization (SDCO) and continuation technique. The performance of accuracy and convergence for all the proposed methods are demonstrated in the numerical simulations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In compressed sensing, the sensing matrix is assumed perfectly known. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. | background 0.93 | 0.07 | 0.02 | asserted 1.00 |
| s2 | Directions-of-arrival (DoA) estimation with off-grid effect satisfies this situation, and can be formulated into a (non)convex optimization problem with linear inequalities constraints, which can be solved by the interior point method (using the CVX tools), but at a large computational cost. | background 0.99 | 0.14 | 0.05 | asserted 0.99 |
| s3 | In this work, in order to design efficient algorithms, we consider various alternative formulations, such as unconstrained formulation, primal-dual formulation, or conic formulation to develop group-sparsity promoted solvers. | contribution 0.69 | 0.84 | 0.07 | asserted 0.90 |
| s4 | First, the consensus alternating direction method of multipliers (C-ADMM) is applied. | method 0.90 | 0.87 | 0.03 | asserted 1.00 |
| s5 | Then, iterative algorithms for the BPDN formulation is proposed by combining the Nesterov smoothing technique with accelerated proximal gradient method, and the convergence analysis of the method is conducted as well. | method 0.60 | 0.93 | 0.07 | asserted 1.00 |
| s6 | We also developed a variant of EGT (Excessive Gap Technique)-based primal-dual method to systematically reduce the smoothing parameter sequentially. | method 0.72 | 0.94 | 0.05 | asserted 1.00 |
| s7 | Finally, we propose algorithms for quadratically constrained L2-L1 mixed norm minimization problem by using the smoothed dual conic optimization (SDCO) and continuation technique. | method 0.61 | 0.94 | 0.09 | asserted 1.00 |
| s8 | The performance of accuracy and convergence for all the proposed methods are demonstrated in the numerical simulations. | result 0.94 | 0.94 | 0.50 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid effect satisfies this situation, and can be formulated into a (non)convex optimization problem with linear inequalities constraints, which can be solved by the interior point method (using the CVX tools), but at a large computational cost. In this work, in order to design efficient algorithms, we consider various alternative formulations, such as unconstrained formulation, primal-dual formulation, or conic formulation to develop group-sparsity promoted solvers. First, the consensus alternating direction method of multipliers (C-ADMM) is applied. Then, iterative algorithms for the BPDN formulation is proposed by combining the Nesterov smoothing technique with accelerated proximal gradient method, and the convergence analysis of the method is conducted as well. We also developed a variant of EGT (Excessive Gap Technique)-based primal-dual method to systematically reduce the smoothing parameter sequentially. Finally, we propose algorithms for quadratically constrained L2-L1 mixed norm minimization problem by using the smoothed dual conic optimization (SDCO) and continuation technique. The performance of accuracy and convergence for all the proposed methods are demonstrated in the numerical simulations.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 2 sentences without a confident label
Compares with 1 paper
-
Note that our first proposed Nesterov smoothing method is equivalent to the one in [ref] , as can be deduced from the results of [ref] .
PRISMA: PRoximal Iterative SMoothing Algorithm · Introduction · 0.91
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.