Abstract
We propose an adaptive weighted high frequency iterative algorithm for a fractional-order total variation (FrTV) approach with nonlocal regularization to alleviate image deterioration and to eliminate staircase artifacts, which result from the total variation (TV) method. The high frequency gradients are reweighted in iterations adaptively when we decompose the image into high and low frequency components using the pre-processing technique. The nonlocal regularization is introduced into our method based on nonlocal means (NLM) filtering, which contains prior image structural information to suppress staircase artifacts. An alternating direction multiplier method (ADMM) is used to solve the problem combining reweighted FrTV and nonlocal regularization. Experimental results show that both the peak signal-to-noise ratios (PSNR) and structural similarity index (SSIM) of reconstructed images are higher than those achieved by the other four methods at various sampling ratios less than 25%. At 5% sampling ratios, the gains of PSNR and SSIM are up to 1.63 dB and 0.0114 from ten images compared with reweighted total variation with nuclear norm regularization (RTV-NNR). The improved approach preserves more texture details and has better visual effects, especially at low sampling ratios, at the cost of taking more time.
Highlights
Compressed sensing (CS) [1,2] is an emerging framework for data acquisition and reconstruction, which permits us to reconstruct the original sparse or compressible signals from only a small number of linear measurements
This is based on the principle that, through optimization, the sparsity of a signal can be recovered from far fewer samples than required by the Nyquist–Shannon sampling theorem when the measurement matrix satisfies the restricted isometry property (RIP) [6]
The most notable application, the single-pixel imaging system, reconstructed images from only a small amount of data from a single photodetector, with the result that it implements the mixing of image signals with a random mask such as the Hadamard matrix generated by a digital micromirror device (DMD) [7]
Summary
Compressed sensing (CS) [1,2] is an emerging framework for data acquisition and reconstruction, which permits us to reconstruct the original sparse or compressible signals from only a small number of linear measurements. The regions which have large gradients (e.g., texture details) have small penalty and the others have large penalty This method preserves the image edges effectively. To improve the quality of reconstructed images, another strategy is nonlocal regularization based on nonlocal means (NLM) filtering This strategy is effective for preserving image details and sharp edges by exploiting structural information. We propose an adaptive reweighted fractional-order TV with nonlocal regularization for image reconstruction. This approach improves the TV model and only weights the high frequency gradients by extracting the high frequency components (e.g., texture details) from the images using pre-processing technique [18].
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