Sliced Ridgelet Transform for Image Denoising

Image denoising based on ridgelet transforms gives better result in image denoising than standard wavelet transforms. In this research work, the researcher introduces a new approach for image denoising that is based on ridgelets computed in a localized manner and that is computationally less intensive than curvelets, but similar donising performance. The projection of image at a certain angle is computed at a certain angle, but only on a defined slice of the noisy image. After that, ridgelet transform of each slice is computed , to produce the ridgelet coefficients for an image.The denoising operation corresponds to a simple thresholding of these ridgelet coefficients. The new method for image denoising technique is based on two operations: one is the redundant directional wavelet transform based on the radon transform, and thresholding of the ridgelet coefficient. The image denoising algorithm with the ridgelet transform can be described by the following operations. First , add the noise to an image and than projection(radon transform) is computed at a certain angle of the noise image. After that, the ridgelet transform of this projection of the noise image is computed and the noise component is reduced by simple thresholding of the ridgelet coefficient. Then, the inverse ridgelet transform is computed to get back the denoised version of that projection of slice at the same angle. Although the shape of the reconstructed object can be seen, the reconstructed image is heavily blurred. To counteract this effect, a high pass filter is applied to the sinogram data in the frequency domain. This is achieved by applying a 1-D DFT to the sinogram data for each angle, multiply by the filter, and then using the inverse DFT to reconstruct the data. The simplest form of high pass filter is a ramp. Applying the ramp filter significantly improves the quality of the reconstructed image. However, because the ramp filter emphasises high frequency components of the image, it can cause unwanted noise. To counteract this, several other high-pass filters are commonly used. In this project we are using Adaptive Filtering. The wiener2 function applies a Wiener filter (a type of linear filter) to an image adaptively, tailoring itself to the local image variance. Where the variance is large, wiener2 performs little smoothing. Where the variance is small, wiener2 performs more smoothing. This approach often produces better results than linear filtering. The adaptive filter is more selective than a comparable linear filter, preserving edges and other high-frequency parts of an image. In addition, there are no design tasks; the wiener2 function handles all preliminary computations and implements the filter for an input image. wiener2. However, does require more computation time than linear filtering. Wiener2 works best when the noise is constant-power ("white") additive noise, such as Gaussian noise.