Ultrasound Speckle Reduction via $$L_{0}$$ Minimization

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Speckle reduction is a crucial prerequisite of many computer-aided ultrasound diagnosis and treatment systems. However, most of existing speckle reduction filters concentrate the blurring near features and introduced the hole artifacts, making the subsequent processing procedures complicated. Optimization-based methods can globally distribute such blurring, leading to better feature preservation. Motivated by this, we propose a novel optimization framework based on \(L_{0}\) minimization for feature preserving ultrasound speckle reduction. We observed that the GAP, which integrates gradient and phase information, is extremely sparser in despeckled images than in speckled images. Based on this observation, we propose the \(L_{0}\) minimization framework to remove speckle noise and simultaneously preserve features in ultrasound images. It seeks for the \(L_{0}\) sparsity of the \(\textit{GAP}\) values, and such sparsity is achieved by reducing small \(\textit{GAP}\) values to zero in an iterative manner. Since features have larger \(\textit{GAP}\) magnitudes than speckle noise, the proposed \(L_{0}\) minimization is capable of effectively suppressing the speckle noise. Meanwhile, the rest of \(\textit{GAP}\) values corresponding to prominent features are kept unchanged, leading to better preservation of those features. In addition, we propose an efficient and robust numerical scheme to transform the original intractable \(L_{0}\) minimization into several sub-optimizations, from which we can quickly find their closed-form solutions. Experiments on synthetic and clinical ultrasound images demonstrate that our approach outperforms other state-of-the-art despeckling methods in terms of noise removal and feature preservation.