Non-Convex High-Order TV and ℓ 0-Norm Wavelet Frame-Based Speckle Noise Reduction

Abstract

To obtain natural restorations from the noisy images contaminated by speckle noise, this brief presents a novel hybrid non-convex regularizers model for image denoising. The proposed new variational model closely combines the superiorities of non-convex high-order total variation function and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula> -norm wavelet frame. This combination helps to avoid the staircase artifacts and maintain discontinuities while removing noise. Numerically, by integrating two popular tools: iteratively reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> algorithm and variable splitting method, a modified alternating minimization method is adopted to optimize the resulting minimization problem. Finally, compared with several despeckling methods, numerical experiments indicate the competitive performance of our solver in visual improvement and objective measurement.