Image Deblurring | Inverse Problem | (PnP) ADMM | FISTA | Proximal | Compressed Sensing | python
Comparing Proximal Algorithms (FISTA and ADMM) for image deblurring / restoration with LASSO (L1 penalty) - comparison w.r.t. time complexity (time taken to compute the iterative updates) and image quality improvement (with PSNR):
Input image is blurred / degraded with noise: y = x * h + n, given degraded y and convolution kernel h, restore original x (with deblurring) by solving LASSO problem ||A(x)-b||^2 + λ||x||_1 (where A(x) = h*x and b = y), using proximal point algorithms.
FISTA (First Iterative Shrinkage Thresholding Algorithm) is a faster version of ISTA, which uses majorization-minimization (MM) method / forward-backward splitting for optimization.
Soft Thresholding (Shrinkage):
x = sign(y).max(y - λ/2,0) for L1 penalty.
ADMM (Alternating-Direction Method of Multipliers) altrrnates between updating the primal and auxiliary variables in the augmented Lagrangian iteratively (uses relaxed l1 proximal projection), it obtains much faster convergence compared to FISTA although the quality of the restored image is about the same.
In the very first step of ADMM, the system of linear equations were solved in the Fourier domain (leveraging the convolution theorem).
ADMM was used to restore both corrupted grayscale and color images.
ADMM PnP (Plug and play) allows to use any denoising prior - here an NLM (NonlocalMeans) patch-based denoiser was used.
Here ADMM PnP with NLM performs the best in terms of image quality (PSNR).
Different values of the hyperparameters were used to test the algorithms.
#imageprocessing #imageprocessingpython #python #algorithm #computervision #machinelearning #optimization #sparse #admm
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