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deepmr.prox.wavelet_denoise

deepmr.prox.wavelet_denoise#

deepmr.prox.wavelet_denoise(input, ndim, ths, wv='db4', device=None, non_linearity='soft', level=None)[source]#

Apply orthogonal Wavelet denoising with the \(\ell_1\) norm.

Adapted from :func:deepinv.denoisers.WaveletDenoiser to support complex-valued inputs.

This denoiser is defined as the solution to the optimization problem:

\[\underset{x}{\arg\min} \; \|x-y\|^2 + \gamma \|\Psi x\|_n\]

where \(\Psi\) is an orthonormal wavelet transform, \(\lambda>0\) is a hyperparameter, and where \(\|\cdot\|_n\) is either the \(\ell_1\) norm (non_linearity="soft") or the \(\ell_0\) norm (non_linearity="hard"). A variant of the \(\ell_0\) norm is also available (non_linearity="topk"), where the thresholding is done by keeping the \(k\) largest coefficients in each wavelet subband and setting the others to zero.

The solution is available in closed-form, thus the denoiser is cheap to compute.

Parameters:

  • input (np.ndarray | torch.Tensor) – Input image of shape (…, n_ndim, …, n_0).

  • ndim (int) – Number of spatial dimensions, can be either 2 or 3.

  • ths (float) – Denoise threshold.

  • wv (str, optional) – Wavelet name to choose among those available in pywt. The default is "db4".

  • device (str, optional) – Device on which the wavelet transform is computed. The default is None (infer from input).

  • non_linearity (str, optional) – "soft", "hard" or "topk" thresholding. The default is "soft".

  • level (int, optional) – Level of the wavelet transform. The default is None.

Returns:

output – Denoised image of shape (…, n_ndim, …, n_0).

Return type:

np.ndarray | torch.Tensor

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