mrpro.algorithms.total_variation_denoising

mrpro.algorithms.total_variation_denoising(idata: IData, regularization_dim: Sequence[int], regularization_weight: float | Sequence[float] | Sequence[Tensor], initial_image: Tensor | None = None, max_iterations: int = 100, tolerance: float = 0) → IData[source]
mrpro.algorithms.total_variation_denoising(idata: Tensor, regularization_dim: Sequence[int], regularization_weight: float | Sequence[float] | Sequence[Tensor], initial_image: Tensor | None = None, max_iterations: int = 100, tolerance: float = 0) → Tensor

Apply total variation denoising.

This algorithm solves the problem \(min_x \frac{1}{2}||x - y||_2^2 + \\sum_i l_i ||\nabla_i x||_1\) by using the PDHG-algorithm. \(y\) is the given noisy image, \(l_i\) are the strengths of the regularization along the different dimensions and \(\nabla_i\) is the finite difference operator applied to \(x\) along different dimensions \(i\).

Parameters:

  • idata (IData | Tensor) – input image

  • regularization_dim (Sequence[int]) – Dimensions along which the total variation reguarization is applied (\(i\)).

  • regularization_weight (float | Sequence[float] | Sequence[Tensor]) – Strengths of the regularization (\(l_i\)). If a single values is given, it is applied to all dimensions. If a sequence is given, it must have the same length as regularization_dim.

  • initial_image (Tensor | None, default: None) – Initial image. If None then the target image \(y\) will be used.

  • max_iterations (int, default: 100) – Maximum number of PDHG iterations.

  • tolerance (float, default: 0) – Tolerance of PDHG for relative change of the primal solution; if zero, max_iterations of PDHG are run.

Returns:

the denoised image.