Efficient sampling of graphsignals is essential to graphsignal processing. Recently, blue-noise was introduced as a sampling method that maximizes the separation between sampling nodes leading to high-frequency domi...
详细信息
ISBN:
(纸本)9789082797091
Efficient sampling of graphsignals is essential to graphsignal processing. Recently, blue-noise was introduced as a sampling method that maximizes the separation between sampling nodes leading to high-frequency dominance patterns, and thus, to high-quality patterns. Despite the simple interpretation of the method, blue-noise sampling is restricted to approximately regular graphs. This study presents an extension of blue-noise sampling that allows the application of the method to irregular graphs. Before sampling with a blue-noise algorithm, the approach regularizes the weights of the edges such that the graph represents a regular structure. Then, the resulting pattern adapts the node's distribution to the local density of the nodes. This work also uses an approach that minimizes the strength of the high-frequency components to recover approximately bandlimited signals. The experimental results show that the proposed methods have superior performance compared to the state-of-the-art techniques.
graphsampling strategies require the signal to be relatively sparse in an alternative domain, e.g. bandlimitedness for reconstructing the signal. When such a condition is violated or its approximation demands a large...
详细信息
ISBN:
(纸本)9789082797060
graphsampling strategies require the signal to be relatively sparse in an alternative domain, e.g. bandlimitedness for reconstructing the signal. When such a condition is violated or its approximation demands a large bandwidth, the reconstruction often comes with unsatisfactory results even with large samples. In this paper, we propose an alternative sampling strategy based on a type of overcomplete graph-based dictionary. The dictionary is built from graph filters and has demonstrated excellent sparse representations for graphsignals. We recognize the proposed sampling problem as a coupling between support recovery of sparse signals and node selection. Thus, to approach the problem we propose a sampling procedure that alternates between these two. The former estimates the sparse support via orthogonal matching pursuit (OMP), which in turn enables the latter to build the sampling set selection through greedy algorithms. Numerical results corroborate the role of key parameters and the effectiveness of the proposed method.
We study the optimal sampling set selection problem in sampling a noisy k-bandlimited graphsignal. To minimize the effect of noise when trying to reconstruct a k-bandlimited graphsignal from m samples, the optimal s...
详细信息
ISBN:
(纸本)9781538646595
We study the optimal sampling set selection problem in sampling a noisy k-bandlimited graphsignal. To minimize the effect of noise when trying to reconstruct a k-bandlimited graphsignal from m samples, the optimal sampling set selection problem has been shown to be equivalent to finding a m × k submatrix with the maximum smallest singular value, σ_(min) [3]. As the problem is NP-hard, we present a greedy algorithm inspired by a similar submatrix selection problem known in computer science and to which we add a local search refinement. We show that 1) in experiments, our algorithm finds a submatrix with larger σ_(min) than prior greedy algorithm [3], and 2) has a proven worst-case approximation ratio of 1/(1 + ε)k, where ε is a constant.
暂无评论