Poisson Image Deconvolution and restoration with Adaptive Total Generalized Variation


Abstract:

Image deconvolution and restoration simultaneously for Poisson noise is an important problem in medical imaging systems. In this paper, we study an adaptive total generalized variation (TGV) regularization based approach for deblurring and deconvolving images corrupted by compound Poisson noise. By using smoothed inverse gradient weights, the proposed scheme filters out noise without introducing oscillatory artifacts, thereby allowing for edge preserving restorations. A combination of primal-dual and split Bregman based algorithms is then used for solving the resulting alternating minimizations. Comparison with other adaptive total variation regularization based approaches on synthetic and natural images show our proposed approach obtains better results in terms of signal recovery, low relative error and high structural similarity with latent imagery. Experimental results on a variety natural images as well as on tomography medical images prove the effectiveness and versatility of our regularization model for simultaneous deblurring and Poisson noise removal. Further, compared to related adaptive total variation, framelet regularization models our Poisson image deconvolution with adaptive TGV (PIDTGV) performs better quantitatively.

Example result: Gaussian Blurred and Compound Poisson Noise Added Synthetic Image.


Comparison with Contemporary Total Variation Regularization Schemes

Degraded

RLTV

RLSATV

BPIDFR

PIDTGV

Comparison on a 1D signal taken across the test image:

Convergence of PSF - Gaussian - No noise case - 20 iterations:

GaussianPSF1Dprofiles1_NoNoise_iteration20_PIDTGV.avi

1-D Profiles: (t = 1 --> 20)

GaussianPSF_NoNoise_iteration20_PIDTGV.avi

2-D Surfaces: (t = 1 --> 20)

Convergence of PSF - Gaussian - Noisy case - 20 iterations:

GaussianPSF1D_Noise20_iteration20_PIDTGV.avi

1-D Profiles: (t = 1 --> 20)

GaussianPSF_Noise20_iteration20_PIDTGV.avi

2-D Surfaces: (t = 1 --> 20)

SPECT Result: GIF file with 47 frames - Click on for GIF animation: Input GIF, PIDTGV GIF.

PET Result:

Reference:

V. B. S. Prasath et al., Poisson image deconvolution and restoration with adaptive total generalized variation. In revision, 2022.