VapourSynth-WNNM

Weighted Nuclear Norm Minimization Denoiser for VapourSynth.

Description

WNNM is a denoising algorithm based on block-matching and weighted nuclear norm minimization.

Block matching, which is popularized by BM3D, finds similar blocks and then stacks together in a 3-D group. The similarity between these blocks allows details to be preserved during denoising.

In contrast to BM3D, which denoises the 3-D group based on frequency domain filtering, WNNM utilizes weighted nuclear norm minimization, a kind of low rank matrix approximation. Because of this, WNNM exhibits less blocking and ringing artifact compared to BM3D, but the computational complexity is much higher. This stage is called collaborative filtering in BM3D.

Usage

Prototype:

core.wnnm.WNNM(clip clip[, float[] sigma = 3.0, int block_size = 8, int block_step = 8, int group_size = 8, int bm_range = 7, int radius = 0, int ps_num = 2, int ps_range = 4, bool residual = false, bool adaptive_aggregation = true, clip rclip = None])

• clip:

  The input clip. Must be of 32 bit float format. Each plane is denoised separately.

• sigma:

  Denoising strength of each plane.

• block_size, block_step, group_size, bm_range, radius, ps_num, ps_range:

  Same as those in VapourSynth-BM3D.

• residual:

  Whether to center blocks before collaborative filtering. Default: False.

• adaptive_aggregation:

  Whether to aggregate blocks adaptively. Default: True.

• rclip:

  Reference clip for block matching. Must be of the same dimensions and format as clip.

Implementation

Default values of block_size, block_step, group_size are modified for acceleration.

For spatial denoising, the block-matching implemented is the same as the official implementation, which is similar to that of BM3D without setting a threshold on whether dissimilar blocks should be included in the 3-D group. This is the same strategy implemented in VapourSynth-BM3DCUDA but not in VapourSynth-BM3D.

For temporal denoising, this implementation utilizes the same predictive search proposed by V-BM3D, which is closer to VapourSynth-BM3D (without dissimilar block thresholding) than VapourSynth-BM3DCUDA. The later one implemented a modified temporal predictive search that may finds multiple instances of the same similar block for acceleration.

During collaborative filtering, the official WNNM implementation centers blocks in the 3-D group. This is controlled by the residual parameter and is off by default. The major singular value is untouched when residual is off.

Note: Because of WNNM and the modification, the maximum denoising effect achieved is the best rank-one approximation of the 3-D group when residual is off, or the mean of the group when residual is on, which may not be enough for strong noises. The official implementation uses iterative regularization, which can be easily implemented as

for i in range(num_iterations):
    if i == 0:
        previous = source
    elif i == 1:
        previous = denoised
    else:
        previous = core.std.Expr([source, previous, denoised], "x y - {factor} * z +".format(factor=0.1))
    denoised = WNNM(previous)
# output: `denoised`

The similar blocks are weightedly aggregated by the inverse of the number of non-zero singular values after WNNM, inspired by BM3D. This is controlled by the adaptive_aggregation parameter and is on by default.

The block-matching can be guided by an oracle reference clip rclip in the same manner as ref for BM3D. The collaborative filtering is not guided, unlike BM3D.

Compilation

• On x86_64, oneMKL is required. Vector class library is also required when compiling with AVX2.

  cmake -S . -B build -D CMAKE_BUILD_TYPE=Release \
  -D MKL_LINK=static -D MKL_THREADING=sequential -D MKL_INTERFACE=lp64
  
  cmake --build build
  
  cmake --install build
  

• On Aarch64, ArmPL is required.

Example build process can be found in workflows.

Reference

1. S. Gu, L. Zhang, W. Zuo and X. Feng, "Weighted Nuclear Norm Minimization with Application to Image Denoising," 2014 IEEE Conference on Computer Vision and Pattern Recognition, 2014, pp. 2862-2869.

2. K. Dabov, A. Foi, V. Katkovnik and K. Egiazarian, "Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering," in IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080-2095, Aug. 2007.

3. K. Dabov, A. Foi and K. Egiazarian, "Video denoising by sparse 3D transform-domain collaborative filtering," 2007 15th European Signal Processing Conference, 2007, pp. 145-149.

4. Official implementation

5. VapourSynth-BM3D

6. VapourSynth-BM3DCUDA