Hyperbolic Wavelet-Fisz Denoising for a Model Arising in Ultrasound Imaging

We present an algorithm and its fully data-driven extension for noise reduction in ultrasound imaging. The proposed method computes the hyperbolic wavelet transform of the image, before applying a multiscale variance stabilization technique, via a Fisz transformation. This adapts the wavelet coefficients statistics to the wavelet thresholding paradigm. The use of hyperbolic wavelets makes it possible to recover the image while respecting the anisotropic nature of structural details. The data-driven extension obviates the need for any prior knowledge of the noise model parameters by estimating the noise variance using an isotonic Nadaraya–Watson estimator. Experiments on synthetic and real data demonstrate the potential of the proposed algorithm to recover ultrasound images while preserving tissue details. Furthermore, comparisons with other noise-reduction methods show that our technique is competitive with the state-of-the-art OBNLM filter. Finally, the variance estimation procedure is applied to real images emphasizing the noise model.