It is known that sparse recovery by measurements from random circulant matrices provides good recovery bounds. We generalize this to measurements that arise as a random orbit of a group representation for some finite group G. We derive estimates for the number of measurements required to guarantee the restricted isometry property with high probability. Following this, we present several examples highlighting the role of appropriate representation-theoretic assumptions.

翻译：已知，利用随机循环矩阵的测量进行稀疏恢复能够提供良好的恢复界。我们将此推广至测量来源于某个有限群G的群表示之随机轨道的情形。我们推导了保证受限等距性质以高概率成立所需测量数量的估计。随后，我们提出了若干示例，以阐明适当表示论假设所起的作用。