SIMRES: Similarity of Residual and Noise Distribution for Parameter Estimation in Regularized Restoration


Abstract:

We propose to automatically estimate the regularization parameter in regularization based restoration models such as the total variation (TV)/total generalized variation (TGV) using a similarity criteria using residual and noise distribution (SIMRES). We study a similarity criteria for estimating the parameter by comparing noise and residual distributions across iterations. We prove that the iterative algorithm, with automatic SIMRES parameter estimation, converges to a solution which corresponds to global minimum of TV/TGV minimization. Experimental results indicate that the scheme achieves good denoising with edge preservation when compared to other related schemes. Extensions to color image denoising and deblurring tasks highlight the applicability of our automatic parameter estimation based TV/TGV schemes.

Example denoising results with TV for different λ Values: Gaussian Noise (sigma = sqrt(0.01)) added to Elaine gray scale image. Total variation (TV) regularization results with different fixed parameter (λ) values.

As can be seen below, we start to see structures (salient edges) are lost and the image becomes piecewise smooth as the regularization parameter is increased from λ = 0.1 to λ = 1.

In our work, we study a similarity based criteria between the amount of noise removed given an initial estimate of noise distribution. This provides an automatic way to select the regularization parameter without adhoc or hand-tuned selection.

Compared with other adaptive parameter estimation along with TV regularization function indicates we get superior results in image restoration as shown below.

Comparison with different parameter estimation based Total Variation regularization schemes:

Top row: Noisy and restoration results by LM - Lagrange Multiplier, GCV - Generalized Cross Validation, IG - Inverse Gradient, SIMRES - Our method.

Bottom row: Residual (difference between noisy and restored) images show that SIMRES scheme (TV) obtains a better result and does not remove salient edges.

Medical video data restoration:


Extension of the automatic parameter estimation based TV regularization (SIMRES-TV) to video data is done by including first order differences in the temporal direction.


T1-weighted cardiac MRI axial-transverse & Flow_RP Magnitude of Phase Contrast videos. Videos can be downloaded below.


To Be Added

References:

[1] V. B. S. Prasath, N. N. Hien, D. N. H. Thanh, S. Dvoenko. SIMRES-TV: Noise and residual similarity for parameter estimation in total variation. 4th International Workshop on Photogrammetric and Computer Vision Techniques for Video surveillance, Biometrics and Biomedicine (PSBB), Moscow, Russia, April 2021. Proc. ISPRS International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XLIV-2/W1, 171-176, April 2021. doi:10.5194/isprs-archives-XLIV-2-W1-2021-171-2021

[2] V. B. S. Prasath. SIMRES: Similarity of residual and noise for parameter estimation in regularized restoration. In preparation, 2022.