# An Extended Primal-Dual Algorithm Framework for Nonconvex Problems with Application to Nonlinear Imaging

arXiv: https://arxiv.org/abs/2109.07174 · HTML: https://mlsanity.com/paper/2109.07174/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2021.

## Built on by (most cited first, 3 of 3)

- [Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT](https://mlsanity.com/paper/2305.03330/) (2023)
- [ResDynUNet++: A nested U-Net with residual dynamic convolution blocks for dual-spectral CT](https://mlsanity.com/paper/2512.16140/) (2025)
- [A Dual-domain Refinement Network with FBP-based Jacobian Learning for Sparse-view Dual-Energy CT Material Decomposition](https://mlsanity.com/paper/2606.30159/) (2026)

## Abstract (arXiv)

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated as a nonlinear convex function with respect to the reconstructed image. Using the proposed framework, we put forward six specific iterative schemes, and present their detailed mathematical explanation. We also establish the relationship to existing algorithms. Moreover, under proper assumptions, we analyze the convergence of the schemes for the general model when the optimal dual variable regarding the nonlinear operator is non-vanishing. As a representative, the image reconstruction for spectral computed tomography is used to demonstrate the effectiveness of the proposed algorithm framework. By special properties of the concrete problem, we further prove the convergence of these customized schemes when the optimal dual variable regarding the nonlinear operator is vanishing. Finally, the numerical experiments show that the proposed algorithm has good performance on image reconstruction for various data with non-standard scanning configuration.