Image Denoising Using Local Tangent Space Alignment

We propose a novel image denoising approach, which is based on exploring an underlying (nonlinear) low-dimensional manifold. Using local tangent space alignment (LTSA), we 'learn' such a manifold, which approximates the image content effectively. The denoising is performed by minimizing a newly defined objective function, which is a sum of two terms: (a) the difference between the noisy image and the denoised image, (b) the distance from the image patch to the manifold. We extend the LTSA method from manifold learning to denoising. We introduce the local dimension concept that leads to adaptivity to different kind of image patches, e.g. flat patches having lower dimension. We also plug in a basic denoising stage to estimate the local coordinate more accurately. It is found that the proposed method is competitive: its performance surpasses the K-SVD denoising method.