arXiv subjects

Jianqing Jia

Publications and source records attributed to Jianqing Jia.

6 recordsLinked to original sources

arXiv2026

Transformed $\ell_1$ Gradient Regularization for Image Denoising

Total variation (TV) regularization is a classical edge-preserving technique widely used across image recovery and reconstruction problems; however, its convex $\ell_1$ gradient penalty tends to over-shrink large gradients, producing staircase artifacts and contrast loss. We propose a gradient-based regularization using the Transformed $\ell_1$ (TL1) penalty and apply it to image denoising. The TL1 penalty asymptotically interpolates between $\ell_1$ and the $\ell_0$ pseudo-norm, offering a principled alternative to TV that better preserves sharp edges and piecewise-smooth regions. Moreover, TL1 admits a tractable proximal operator, enabling an efficient algorithm based on a proximal splitting scheme with subproblems solved by the Alternating Direction Method of Multipliers (ADMM). The weak convexity of TL1 guarantees global convergence of the proximal iterates to a stationary point under mild conditions. Numerical experiments on image denoising demonstrate that the proposed method effectively preserves sharp edges, local contrast, and piecewise-smooth structures, outperforming other gradient-based approaches.

eess.IV↗

arXiv2026

Plug-and-Play Volumetric Reconstruction for Compressive Sensing Light-Sheet Microscopy

We investigate volumetric reconstruction for compressive sensing light-sheet microscopy (CS-LSM), where fast volumetric imaging is achieved by encoding multiple axial planes into each camera exposure. To recover the underlying volume from highly multiplexed measurements, we propose a plug-and-play (PnP) framework that flexibly incorporates any user-specified denoiser into the reconstruction process. Building on a slice-based formulation, we further introduce an axial-coupled model that exploits correlations between adjacent slices to improve volumetric continuity. For efficient computation, we derive a Woodbury-based update for the data-consistency step in both the slice-based and axial-coupled formulations, and employ a Gauss-Seidel sweep for the denoising step in the axial-coupled model. Under a weakly convex regularization assumption, we establish subsequential convergence of the proposed algorithm. Experiments on synthetic and real zebrafish-heart data demonstrate that the proposed framework successfully recovers cellular structures from compressed measurements, and provide practical insights into the comparative performance of commonly used denoisers within the PnP framework under the CS-LSM setup.

cs.CV↗

arXiv2025

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

Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $\ell_1$ to $\ell_2$ norms, $(\ell_1/\ell_2)^2$, has been introduced as a sparsity-prompting function, showing superior performance compared to traditional $\ell_1$ minimization, particularly in challenging scenarios with high coherence and dynamic range. This paper explores the integration of the proximity operator of $(\ell_1/\ell_2)^2$ and $\ell_1/\ell_2$ into efficient optimization frameworks, including the Accelerated Proximal Gradient (APG) and Alternating Direction Method of Multipliers (ADMM). We rigorously analyze the convergence properties of these algorithms and demonstrate their effectiveness in compressed sensing and image restoration applications. Numerical experiments highlight the advantages of our proposed methods in terms of recovery accuracy and computational efficiency, particularly under noise and high-coherence conditions.

math.OC↗

arXiv2024

Sparse Recovery: The Square of $\ell_1/\ell_2$ Norms

This paper introduces a nonconvex approach for sparse signal recovery, proposing a novel model termed the $τ_2$-model, which utilizes the squared $\ell_1/\ell_2$ norms for this purpose. Our model offers an advancement over the $\ell_0$ norm, which is often computationally intractable and less effective in practical scenarios. Grounded in the concept of effective sparsity, our approach robustly measures the number of significant coordinates in a signal, making it a powerful alternative for sparse signal estimation. The $τ_2$-model is particularly advantageous due to its computational efficiency and practical applicability. We detail two accompanying algorithms based on Dinkelbach's procedure and a difference of convex functions strategy. The first algorithm views the model as a linear-constrained quadratic programming problem in noiseless scenarios and as a quadratic-constrained quadratic programming problem in noisy scenarios. The second algorithm, capable of handling both noiseless and noisy cases, is based on the alternating direction linearized proximal method of multipliers. We also explore the model's properties, including the existence of solutions under certain conditions, and discuss the convergence properties of the algorithms. Numerical experiments with various sensing matrices validate the effectiveness of our proposed model.

math.OC↗

arXiv2024

Computing Proximity Operators of Scale and Signed Permutation Invariant Functions

This paper investigates the computation of proximity operators for scale and signed permutation invariant functions. A scale-invariant function remains unchanged under uniform scaling, while a signed permutation invariant function retains its structure despite permutations and sign changes applied to its input variables. Noteworthy examples include the $\ell_0$ function and the ratios of $\ell_1/\ell_2$ and its square, with their proximity operators being particularly crucial in sparse signal recovery. We delve into the properties of scale and signed permutation invariant functions, delineating the computation of their proximity operators into three sequential steps: the $\mathbf{w}$-step, $r$-step, and $d$-step. These steps collectively form a procedure termed as WRD, with the $\mathbf{w}$-step being of utmost importance and requiring careful treatment. Leveraging this procedure, we present a method for explicitly computing the proximity operator of $(\ell_1/\ell_2)^2$ and introduce an efficient algorithm for the proximity operator of $\ell_1/\ell_2$.

math.OC↗

arXiv2019

Semantic-Aware Label Placement for Augmented Reality in Street View

In an augmented reality (AR) application, placing labels in a manner that is clear and readable without occluding the critical information from the real-world can be a challenging problem. This paper introduces a label placement technique for AR used in street view scenarios. We propose a semantic-aware task-specific label placement method by identifying potentially important image regions through a novel feature map, which we refer to as guidance map. Given an input image, its saliency information, semantic information and the task-specific importance prior are integrated into the guidance map for our labeling task. To learn the task prior, we created a label placement dataset with the users' labeling preferences, as well as use it for evaluation. Our solution encodes the constraints for placing labels in an optimization problem to obtain the final label layout, and the labels will be placed in appropriate positions to reduce the chances of overlaying important real-world objects in street view AR scenarios. The experimental validation shows clearly the benefits of our method over previous solutions in the AR street view navigation and similar applications.

cs.CV↗