The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Multidimensional Digital Signal Processing
Multidimensional Digital Signal Processing
Integer to integer mapping wavelet filter bank with adaptive number of zero moments
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A new method for varying adaptive bandwidth selection
IEEE Transactions on Signal Processing
Nonseparable two- and three-dimensional wavelets
IEEE Transactions on Signal Processing
Performance analysis of the adaptive algorithm for bias-to-variance tradeoff
IEEE Transactions on Signal Processing
Adaptive lifting schemes with perfect reconstruction
IEEE Transactions on Signal Processing
Wavelet families of increasing order in arbitrary dimensions
IEEE Transactions on Image Processing
Adaptive polyphase subband decomposition structures for image compression
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Nonlinear wavelet transforms for image coding via lifting
IEEE Transactions on Image Processing
Design of signal-adapted multidimensional lifting scheme for lossy coding
IEEE Transactions on Image Processing
A 2-D orientation-adaptive prediction filter in lifting structures for image coding
IEEE Transactions on Image Processing
Directionlets: anisotropic multidirectional representation with separable filtering
IEEE Transactions on Image Processing
Adaptive Directional Lifting-Based Wavelet Transform for Image Coding
IEEE Transactions on Image Processing
Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images
IEEE Transactions on Image Processing
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In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.