TY - JOUR
T1 - High-Resolution Image Reconstruction: An env$_{\ell ^1} $/TV Model and a Fixed-Point Proximity Algorithm
AU - W.-T. Long, Y. Lu, L.-X. Shen & Y.-S. Xu
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 255
EP - 282
PY - 2016
DA - 2016/05
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/420.html
KW - High-resolution image reconstruction, env$_{\ell^1}$/TV model, proximity operator, fixed-point algorithm.
AB - <p style="text-align: justify;">High-resolution image reconstruction obtains one high-resolution image from multiple low-resolution, shifted, degraded samples of a true scene. This is a typical ill-posed problem and optimization
models such as the $\ell^2$/TV model are previously studied for solving this problem. It is based on the assumption that during acquisition digital images are polluted by Gaussian noise. In this work, we propose
a new optimization model arising from the statistical assumption for mixed Gaussian and impulse noises,
which leads us to choose the Moreau envelop of the $\ell^1$-norm as the fidelity term. The developed env$_{\ell^1}$/TV
model is effective to suppress mixed noises, combining the advantages of the $\ell^1$/TV and the $\ell^2$/TV models.
Furthermore, a fixed-point proximity algorithm is developed for solving the proposed optimization model
and convergence analysis is provided. An adaptive parameter choice strategy for the developed algorithm is
also proposed for fast convergence. The experimental results confirm the superiority of the proposed model
compared to the previous $\ell^2$/TV model besides the robustness and effectiveness of the derived algorithm.</p>