Fast Harmonic and Sparse Image Decomposition Model and Its Application
ZHENG Cheng-Yong
School of Mathematics and Computating Science, Wuyi University, Jiangmen 529020 School of Automation, Huazhong University of Science and Technology, Wuhan 430074
Abstract An image decomposition model, harmonic and sparse image decomposition (HSID), is firstly put forward to decompose an image into a harmonic component and a sparse component. Then, based on augmented Lagrangian alternating direction method (ALADM), an algorithm, namely HSID_ALADM, is presented to solve HSID. The main computational load of each iteration in HSID_ALADM is computing fast Fourier transform (FFT), which makes HSID_ALADM fast. HSID_ALADM can be used to decompose an infrared image with small targets into a harmonic component and a sparse component. The harmonic component is considered as the modeling of the background, and the sparse component as the small target component. By searching for the maximum local energy regions in the sparse component, the infrared targets in the infrared image can be easily and accurately located. Experimental results of small infrared target detection for real infrared images and image completion and inpainting show good performance of HSID_ALAD.
2014, Vol. 27 
