Semi-Sparsity for Smoothing Filters
This work addresses signal/image processing and computer vision applications by introducing a novel method for smoothing, though it appears incremental as it builds on existing sparsity and optimization frameworks.
The paper tackles the problem of smoothing filters where sparsity is not fully applicable, such as polynomial-smoothing surfaces, by proposing a semi-sparsity smoothing algorithm based on a generalized L0-norm minimization in higher-order gradient domains, resulting in a feature-aware filtering method that handles both sparse and non-sparse regions.
In this paper, we propose an interesting semi-sparsity smoothing algorithm based on a novel sparsity-inducing optimization framework. This method is derived from the multiple observations that semi-sparsity prior knowledge is more universally applicable, especially in areas where sparsity is not fully admitted, such as polynomial-smoothing surfaces. We illustrate that this semi-sparsity can be identified into a generalized $L_0$-norm minimization in higher-order gradient domains, thereby giving rise to a new "feature-aware" filtering method with a powerful simultaneous-fitting ability in both sparse features (singularities and sharpening edges) and non-sparse regions (polynomial-smoothing surfaces). Notice that a direct solver is always unavailable due to the non-convexity and combinatorial nature of $L_0$-norm minimization. Instead, we solve the model based on an efficient half-quadratic splitting minimization with fast Fourier transforms (FFTs) for acceleration. We finally demonstrate its versatility and many benefits to a series of signal/image processing and computer vision applications.