中文摘要：

首先提出一种图像调和稀疏分解（HSID）模型，用于将一幅图像分解为调和分量和稀疏分量．然后提出基于增广拉格朗日交替方向法（ALADM）的HSID求解算法（HSID_ALADM），算法每次迭代的主要计算量为矩阵的快速傅氏变换，因此HSID_ALADM快速高效．将HSID_ALADM用于红外图像分解，所得的调和分量可视为图像背景，而其稀疏分量可视为图像中的目标分量，通过搜索稀疏分量中的局部能量极值，可检测出红外图像中的小目标．HSID_ALADM亦可直接用于图像补全与修复．实际的红外图像目标检测及图像补全与修复实验表明HSID_ALADM性能良好．

英文摘要：

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.