The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Estimation of noise in images: an evaluation
CVGIP: Graphical Models and Image Processing
Analog and Digital Signal Processing
Analog and Digital Signal Processing
The steerable pyramid: a flexible architecture for multi-scale derivative computation
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 3)-Volume 3 - Volume 3
Noise Estimation from a Single Image
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Training methods for image noise level estimation on wavelet components
EURASIP Journal on Applied Signal Processing
Removal of correlated noise by modeling the signal of interest in the wavelet domain
IEEE Transactions on Image Processing
A note on the discrete wavelet transform of second-order processes
IEEE Transactions on Information Theory
Noise Covariance Properties in Dual-Tree Wavelet Decompositions
IEEE Transactions on Information Theory
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid
IEEE Transactions on Image Processing
Fast and reliable structure-oriented video noise estimation
IEEE Transactions on Circuits and Systems for Video Technology
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This correspondence deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function or alternatively the power spectral density (PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of "blind" wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem.