Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most practical application. We try to close this gap by showing how the sparsity patterns can instead be characterised via a probability distribution on the supports of the sparse signals allowing us to again derive optimal subsampling strategies. This probability distribution can be easily estimated from signals of the same signal class, achieving state of the art performance in numerical experiments. Our approach also extends to structured acquisition, where instead of isolated measurements, blocks of measurements are taken.

翻译：近期压缩感知领域的研究表明，最优欠采样策略需考虑信号本身的稀疏模式。这种预知性知识虽具理论价值，但在实际应用中仍难以获取。本文通过建立稀疏信号支撑集上的概率分布模型来表征稀疏模式，从而重新推导出最优欠采样策略，弥补了上述理论空白。该概率分布可通过同类信号样本高效估计，在数值实验中取得了当前最优性能。本方法还可推广至结构化采集场景，即采用测量块而非独立测量点进行数据获取。