• Geophysics and Geophysical Exploration
• /
• v.10 no.2
• /
• pp.124-130
• /
• 2007

Least squares ($l^2$ norm) solutions of seismic inversion tend to be very sensitive to data points with large errors. The $l^1$ norm minimization gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) method gives efficient approximate solutions of these $l^1$ norm problems. I propose an efficient implementation of the IRLS method for a hybrid $l^1/l^2$ minimization problem that behaves as $l^2$ norm fit for small residual and $l^1$ norm fit for large residuals. The proposed algorithm shows more robust characteristics to the decision of the threshold value than the l1 norm IRLS inversion does with respect to the threshold value to avoid singularity.

• 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 the Acoustical Society of Korea
• /
• v.36 no.5
• /
• pp.293-299
• /
• 2017

Small unmanned platforms maneuvering underwater are the key naval future forces, utilized as the asymmetric power in war. As a method of detecting and identifying such platforms, we introduce a property estimation technique based on an iterative numerical analysis. The property estimation technique can estimate not only the position of a target but also its physical properties. Moreover, it will have a potential in detecting and classifying still target or multiple targets. In this study, we have conducted the property estimation of an small underwater target using the data acquired from the lake experiment. As a result, it shows that the properties of a small platform may be roughly estimated from the in site data even using one channel.