Lixin Shen

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math.OC2026

Explicit Series and a Certified Hybrid Evaluator for the $ℓ_{p}$ Proximity Operator for $0 < p < 1$

Lixin Shen, Jiangyu Yu

The nonconvex $ℓ_{p}$ quasi-norm with $0 < p < 1$ is a powerful sparsity surrogate but makes the proximity operator $prox_{λ ∣ \cdot ∣^{p}}$ nontrivial to evaluate robustly. We gi…

math.OC2025

Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions

Jianqing Jia, Ashley Prater-Bennette, Lixin Shen

Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $ℓ_{1}$ to $ℓ_{2}$ norms, $(ℓ_{1} / ℓ_{2})^{2}$ , has be…

math.OC2024

Sparse Recovery: The Square of $ℓ_{1} / ℓ_{2}$ Norms

Jianqing Jia, Ashley Prater-Bennette, Lixin Shen +1

This paper introduces a nonconvex approach for sparse signal recovery, proposing a novel model termed the $τ_{2}$ -model, which utilizes the squared $ℓ_{1} / ℓ_{2}$ norms for this pur…

math.OC2024

Computing Proximity Operators of Scale and Signed Permutation Invariant Functions

Jianqing Jia, Ashley Prater-Bennette, Lixin Shen

This paper investigates the computation of proximity operators for scale and signed permutation invariant functions. A scale-invariant function remains unchanged under uniform scal…

Explicit Series and a Certified Hybrid Evaluator for the ℓp​ Proximity Operator for 0<p<1

Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions

Sparse Recovery: The Square of ℓ1​/ℓ2​ Norms

Computing Proximity Operators of Scale and Signed Permutation Invariant Functions

Explicit Series and a Certified Hybrid Evaluator for the $ℓ_{p}$ Proximity Operator for $0 < p < 1$

Sparse Recovery: The Square of $ℓ_{1} / ℓ_{2}$ Norms