Image Denoising With Edge-Preserving and Segmentation Based on Mask NHA.

In this paper, we propose a zero-mean white Gaussian noise removal method using a high-resolution frequency analysis. It is difficult to separate an original image component from a noise component when using discrete Fourier transform or discrete cosine transform for analysis because sidelobes occur in the results. The 2D non-harmonic analysis (2D NHA) is a high-resolution frequency analysis technique that improves noise removal accuracy because of its sidelobe reduction feature. However, spectra generated by NHA are distorted, because of which the signal of the image is non-stationary. In this paper, we analyze each region with a homogeneous texture in the noisy image. Non-uniform regions that occur due to segmentation are analyzed by an extended 2D NHA method called Mask NHA. We conducted an experiment using a simulation image, and found that Mask NHA denoising attains a higher peak signal-to-noise ratio (PSNR) value than the state-of-the-art methods if a suitable segmentation result can be obtained from the input image, even though parameter optimization was incomplete. This experimental result exhibits the upper limit on the value of PSNR in our Mask NHA denoising method. The performance of Mask NHA denoising is expected to approach the limit of PSNR by improving the segmentation method.

Image inpainting on the basis of spectral structure from 2-D nonharmonic analysis.

The restoration of images by digital inpainting is an active field of research and such algorithms are, in fact, now widely used. Conventional methods generally apply textures that are most similar to the areas around the missing region or use a large image database. However, this produces discontinuous textures and thus unsatisfactory results. Here, we propose a new technique to overcome this limitation by using signal prediction based on the nonharmonic analysis (NHA) technique proposed by the authors. NHA can be used to extract accurate spectra, irrespective of the window function, and its frequency resolution is less than that of the discrete Fourier transform. The proposed method sequentially generates new textures on the basis of the spectrum obtained by NHA. Missing regions from the spectrum are repaired using an improved cost function for 2D NHA. The proposed method is evaluated using the standard images Lena, Barbara, Airplane, Pepper, and Mandrill. The results show an improvement in MSE of about 10-20 compared with the examplar-based method and good subjective quality.

Motion analysis using 3D high-resolution frequency analysis.

The spatiotemporal spectra of a video that contains a moving object form a plane in the 3D frequency domain. This plane, which is described as the theoretical motion plane, reflects the velocity of the moving objects, which is calculated from the slope. However, if the resolution of the frequency analysis method is not high enough to obtain actual spectra from the object signal, the spatiotemporal spectra disperse away from the theoretical motion plane. In this paper, we propose a high-resolution frequency analysis method, described as 3D nonharmonic analysis (NHA), which is only weakly influenced by the analysis window. In addition, we estimate the motion vectors of objects in a video using the plane-clustering method, in conjunction with the least-squares method, for 3D NHA spatiotemporal spectra. We experimentally verify the accuracy of the 3D NHA and its usefulness for a sequence containing complex motions, such as cross-over motion, through comparison with 3D fast Fourier transform. The experimental results show that increasing the frequency resolution contributes to high-accuracy estimation of a motion plane.