Total Variation Denoising

MATLAB functions:  tv.m  calc_lam.m  calc_lamxy.m  loc_var.m  db.m    

• TV denoising (scalar fidelity term) [ROF92]

Reduces the total-variation of the image. Filters out noise while preserving edges. Textures and fine-scale details are also removed. In this demo the assumption is that a white Gaussian noise is added with a-priori known (or estimated) noise power (variance). The fidelity term to the input image is calculated automatically so that the power of the noise is reduced.

MATLAB code:  demo_tv.m

             
              Noisy input           Filtered by TV

• Texture preserving TV (adaptive fidelity term) [GSZ03]

  Reduces selectively the total-variation of the image. Generalization of the TV process to adaptive power constraints. Denoising is strong in smooth regions and weaker in textured regions.  Preserves better texture and fine-scale details. This is a two-phase process where the noise and textures are first isolated by scalar TV. The adaptive process  then imposes local power constraints based on local variance measures of the first phase.

  MATLAB code: demo_adap_tv.m  

  Image: toys.bmp 

               

             Noisy input            Scalar TV         Adaptive TV

[ROF92] L. Rudin, S. Osher, E. Fatemi, ``Nonlinear Total Variation based noise removal algorithms", Physica D 60 259-268,`92.
[GSZ03] Guy Gilboa, Nir Sochen, Yehoshua Y. Zeevi, "Texture Preserving Variational Denoising Using an Adaptive Fidelity Term", to appear in Proc. VLSM 2003, Nice, France, Oct. 2003.PDF  

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02-09-2003