A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple-order derivatives for detecting local image characteristics
Computer Vision, Graphics, and Image Processing
The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deblurring digital images by means of polynomial transforms
Computer Vision, Graphics, and Image Processing
A quantitative comparison of edge-preserving smoothing techniques
Signal Processing
Gabor phase in texture discrimination
Signal Processing
Image Filtering Using Multiresolution Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Image Enhancement and Noise Filtering by Use of Local Statistics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computers and Electrical Engineering
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We present two related algorithms for reducing noise in computerized tomography images. The algorithms are based on a recently developed technique for image representation called a polynomial transform. With this technique it is possible to decompose the image into local components, perform nonlinear and adaptive processing on these components, and resynthesize the image from the processed components. In this paper we describe how this can be applied to adapt the amount of noise reduction to the local image content. In the first algorithm, a single polynomial transform is used to perform the noise reduction. A critical parameter of this algorithm is the size of the local components. No single size is optimal for the entire image, so a compromise has to be made. An alternative approach is adopted in the second algorithm, where several polynomial transforms are used in parallel at different resolutions. This allows for a better adaptation of the size of the image components used in the reconstruction to the original image. For instance, uniform regions containing only noise are described with large-sized components. Low-contrast edges are restored with medium-sized components, while high-contrast edges contain high-resolution components.