AVSS 2026 · Image restoration

An Improved Variational Method for Image Denoising

Jing-En Huang^1,*, Jia-Wei Liao^2,*, Ku-Te Lin^3,*, Yu-Ju Tsai^1,*, Mei-Heng Yueh^4,†

¹National Yang Ming Chiao Tung University · ²National Taiwan University · ³National Central University · ⁴National Taiwan Normal University

* Equal contribution · † Corresponding author

MixTV unifies total variation with L1 and L2 data fidelity, preserving edges while remaining robust to sparse, dense, and mixed noise—without training data.

Read paper Supplement Poster arXiv Results repository ↗

The idea

One model for mixed noise.

Classical fidelity terms are often tailored to a single noise family. MixTV combines their complementary strengths in one strictly convex variational objective, then solves it efficiently with split Bregman iteration.

Why mixed fidelity?

Real corruption rarely follows one clean distribution.

Sensors, transmission, and post-processing can introduce both impulsive and distributed errors into the same image.

Sparse noiseImpulse-like outliers are handled robustly by L1 fidelity.

Dense noiseDistributed perturbations are modeled effectively by L2 fidelity.

MixTV objective

Edge-aware regularization meets dual data fidelity.

u* = arg min_u { ‖D_xu‖₁ + ‖D_yu‖₁ + μ‖u − f‖₁ + α‖u − f‖₂² }

Anisotropic TVSuppresses oscillations while retaining sharp image structures.

L1 fidelityLimits the influence of sparse, high-magnitude outliers.

L2 fidelityStabilizes recovery under dense perturbations and ensures strict convexity.

Step 01Split variables

Decouple spatial gradients and the nonsmooth fidelity term with auxiliary variables.

Step 02Solve for u

Update the image through a structured linear system formed by the difference operators.

Step 03Shrink

Apply componentwise soft thresholding to the split gradient and fidelity variables.

Step 04Bregman update

Update the residual variables and repeat until the stopping tolerance is met.

Guarantee 01

Unique minimizer

The positive quadratic fidelity term makes the objective strictly convex, so the denoised solution is unique.

Guarantee 02

Convergent iteration

The supplementary analysis establishes vanishing residuals, bounded iterates, and convergence of the split Bregman scheme.

Quantitative evaluation

Consistent across noise types.

Experiments use four 250 × 250 benchmark images and 25 single or ordered mixed-noise settings. Performance is measured by PPS = PSNR × SSIM; higher is better.

Table I

PPS comparison of image denoising methods

Scores are averaged over the four benchmark images. Higher is better.

Noise type	Noisy	1-norm	Isotropic	Anisotropic	1-norm + Isotropic	1-norm + Anisotropic	Isotropic + 1-norm	Anisotropic + 1-norm	DnCNN	MixTV (Ours)
Gaussian	16.16	19.41	9.00	8.53	9.21	8.74	8.99	8.53	21.87	21.15
S&P	11.58	20.48	9.03	8.54	6.52	9.12	9.02	8.54	15.86	22.84
Poisson	26.33	22.51	9.60	9.04	9.54	9.03	9.59	9.04	28.21	24.86
speckle	14.44	17.52	9.09	8.56	9.08	8.62	9.08	8.55	21.07	19.42
uniform	11.00	18.66	8.49	8.04	6.46	9.03	8.48	8.04	16.81	21.67
Gaussian + S&P	9.53	18.04	8.51	8.06	9.18	8.71	8.50	8.06	16.36	19.29
Gaussian + Poisson	15.10	18.88	8.92	8.45	9.11	8.64	8.91	8.44	21.15	20.51
Gaussian + speckle	10.80	15.96	8.47	8.03	8.66	8.24	8.46	8.03	18.11	17.39
Gaussian + uniform	9.03	15.79	7.99	7.59	8.78	8.37	7.99	7.59	15.92	17.61
S&P + Gaussian	9.87	17.93	8.49	8.05	9.12	8.67	8.48	8.05	16.60	19.17
S&P + Poisson	11.23	19.82	8.92	8.45	9.51	8.99	8.92	8.45	16.62	21.94
S&P + speckle	9.11	16.64	8.46	8.02	9.00	8.54	8.45	8.02	15.91	18.18
S&P + uniform	7.73	17.48	7.99	7.59	6.46	9.00	7.99	7.59	14.51	20.12
Poisson + Gaussian	15.04	18.80	8.93	8.46	9.12	8.65	8.92	8.46	21.16	20.41
Poisson + S&P	11.06	19.71	8.94	8.46	9.52	9.00	8.93	8.46	16.57	21.99
Poisson + speckle	13.71	17.08	9.01	8.50	8.98	8.53	9.00	8.49	20.49	18.88
Poisson + uniform	10.49	17.94	8.40	7.96	9.36	8.86	8.40	7.96	16.81	20.71
speckle + Gaussian	10.88	16.04	8.44	8.00	8.65	8.23	8.43	8.00	18.01	17.44
speckle + S&P	8.82	16.71	8.48	8.04	9.04	8.59	8.47	8.04	15.60	18.23
speckle + Poisson	13.90	17.15	8.96	8.44	8.92	8.47	8.96	8.44	20.45	18.94
speckle + uniform	8.37	15.40	7.95	7.55	8.71	8.28	7.95	7.55	15.36	17.09
uniform + Gaussian	9.01	15.88	8.01	7.60	8.81	8.40	8.00	7.60	15.90	17.65
uniform + S&P	7.64	17.55	8.01	7.60	6.47	9.01	8.00	7.60	14.49	20.20
uniform + Poisson	10.49	18.05	8.39	7.95	9.36	8.86	8.38	7.95	16.79	20.72
uniform + speckle	8.33	15.40	7.96	7.57	8.71	8.29	7.95	7.57	15.30	17.09

Full experiment explorer

Inspect every comparison.

Choose a benchmark and noise process to compare the noisy input, seven established variational baselines, and the proposed mixed-norm model. Noise combinations use “+” consistently with Table I.

Dog · Salt & pepper + Poisson

Experiment 11 of 25

Denoising comparison on the dog benchmark with salt-and-pepper plus Poisson noise

Panels: original, noisy input, seven variational baselines, and the proposed mixed-norm model.Open large image ↗

View all 25 Dog results

Citation

Build on MixTV.

If this work supports your research, please cite the paper and link back to this project page.

View on arXiv ↗ Result files ↗

BibTeX

@article{huang2024improved,
  title   = {An Improved Variational Method for Image Denoising},
  author  = {Huang, Jing-En and Liao, Jia-Wei and Lin, Ku-Te and
             Tsai, Yu-Ju and Yueh, Mei-Heng},
  journal = {arXiv preprint arXiv:2410.02587},
  year    = {2024}
}