OMP算法对稀疏信号准确重构的一个充分条件

A Sufficient Condition for Sparse Signals' Exact Recovery by Using OMP Algorithm

压缩感知的研究对象是稀疏信号,那么在什么条件下以及采用何种方法能准确地重构一个稀疏信号自然成为人们关注的问题.在带有噪声的情形下,如果观测矩阵满足受限等距性质以及受限等距常数δk+kδk+1<1,并且噪声强度一定的条件下,证明了对任意的k-稀疏向量x,正交匹配追踪(OMP)算法可以通过k步迭代准确重构原信号.

Compressed sensing is often applied to sparse signals.Naturally,what the researchers are often concerned is whether a sparse signal can be recovered exactly under proper conditions and with proper methods.Here a noisy case is considered to show that if the compressed sensing matrix satisfies the restricted isometry property with restricted isometry constantδk+kδk+1<1and the noise is constrained,then a greedy algorithm called Orthogonal Matching Pursuit(OMP)can recover the signal with knonzero entries in kiterations.