基于最小二乘增量迭代正则化方法的图像复原

Image restoration based on least-squares increment iterative and regularization method

针对模糊图像的复原问题,从最小二乘算法出发,采用增量迭代的方法改善算法的收敛性,同时结合正则化技术克服问题的病态性质,研究了一种有效的图像复原方法。在运算中,采用最速下降法求解方程,并运用快速傅立叶变换(FFT)原理来减少计算复杂度,同时引入自适应的正则化参数,使其与图像复原的迭代运算同步进行并自动修正到最优值。计算机仿真结果表明,该方法可较好地再现原图像的重要信息,复原图像在峰值信噪比和主观视觉效果方面都有明显的提高。

Aiming at the restoration of blurred image, an effective restoration approach based on least-square algorithm was proposed. This method adopted increment iterative algorithm to improve convergence and meanwhile applied regularization technique to overcome ill-posed problem. In the computations, the equation was solved by steepest descend algorithm, and the complexity was reduced by FFT principal, meanwhile, the regularization parameter has its adaptive character, which can be determined in terms of the restored image at each iteration step therefore automatically correct to the appropriate value. Computer simulations show that the proposed method can properly retrieve the main information of original image, and the PSNR （peak signal to noise ratio） and subjective visual effect of the restored image are improved significantly.