O(1) Algorithms for Overlapping Group Sparsity

Sparsity based techniques have become very popular in machine learning, medical imaging and computer vision. Recently, with the emerging and development of structured sparsity, signals can be recovered more accurately. However, solving structured sparsity problems often involves much higher computational complexity. Few of existing works can reduce the computational complexity of such problems. Especially for overlapping group sparsity, the computational complexity for each entry is linear to the degree of overlapping, making it infeasible for large-scale problems. In this paper, we propose novel algorithms to efficiently address this issue, where the computational complexity for each entry is always O(1) and independent to the degree of overlapping. Experiments on 1D signal and 2D image demonstrate the effectiveness and efficiency of our methods. This work may inspire more scalable algorithms for structured sparsity.