• 한국지구물리탐사학회:학술대회논문집
• /
• 2005.05a
• /
• pp.227-232
• /
• 2005

Least squares (${\ell}^2-norm$) solutions of seismic inversion tend to be very sensitive to data points with large errors. The ${\ell}^p-norm$ minimization for $1{\le}p<2$ gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions of these ${\ell}^p-norm$ problems. I propose a simple way to implement the IRLS method for a hybrid ${\ell}^1/{\ell}^2$ minimization problem that behaves as ${\ell}^2$ fit for small residual and ${\ell}^1$ fit for large residuals. Synthetic and a field-data examples demonstrates the improvement of the hybrid method over least squares when there are outliers in the data.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.28 no.8
• /
• pp.636-645
• /
• 2017

A scanning radar is exploited widely such as for ground surveillance, disaster rescue, and etc. However, the range resolution is limited by transmitted bandwidth and cross-range resolution is limited by beam width. In this paper, we propose a method for super-resolution radar imaging. If the distribution of reflectivity is sparse, the distribution is called sparse signal. That is, the problem could be formulated as compressive sensing problem. In this paper, 2D super-resolution radar image is generated via reweighted ${\ell}_1-Minimization$. In the simulation results, we compared the images obtained by the proposed method with those of the conventional Orthogonal Matching Pursuit(OMP) and Synthetic Aperture Radar(SAR).

• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.1
• /
• pp.41-55
• /
• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.