Unit norm tight frames are useful in providing stable reconstruction. Incoherence, restricted isometry property and statistical restricted isometry property of a frame provide performance guarantees of sparse signal recovery algorithms in compressed sensing. Equiangular tight frames, mutually unbiased bases and chirp matrices are well known incoherent unit norm tight frames that exhibit near optimal sparse recovery guarantees. The dimension of frame elements belongs to some particular family of numbers and the number of elements in these frames is in the order of square of the dimension of the underlying space. In the present work, we construct incoherent unit norm tight frames for more general dimensions with higher redundancy than these frames. One of the important features of our construction is that it produces incoherent unit norm tight frames that are a union of orthonormal bases. In addition, the incoherent unit norm tight frames that we construct possess the statistical restricted isometry property and statistical incoherence property. As a result they exhibit near optimal theoretical guarantees in recovering sparse signals obtained from a generic random signal model. Using simulations, we demonstrate the efficacy of the constructed tight frames as good candidates for recovering sparse signals as against partial Fourier matrices and with existing constructions of incoherent unit norm tight frames.

单位规范紧密框架可用于提供稳定的重建。帧的非相干性，受限等距特性和统计受限等距特性为压缩感知中的稀疏信号恢复算法提供了性能保证。等角的紧密框架，相互无偏的基和rp矩阵是众所周知的非相干单位范式紧密框架，其表现出接近最佳的稀疏恢复保证。框架元素的尺寸属于某些特定的数字族，并且这些框架中的元素数量约为基础空间尺寸的平方。在当前的工作中，我们构造了非相干单位范数紧框架，以用于比这些框架具有更高冗余度的更一般的尺寸。我们的结构的重要特征之一是，它会产生不连贯的单位规范紧密框架，这些框架是正交基准的并集。此外，我们构建的非相干单元范数紧框架具有统计受限的等距性质和统计非相干性质。结果，它们在恢复从通用随机信号模型获得的稀疏信号方面显示出接近最佳的理论保证。使用模拟，我们证明了构造的紧框架是恢复稀疏信号的良好候选者的有效性，相对于部分傅立叶矩阵，以及现有的非相干单位范式紧框架的构造。我们构造的非相干单元范数紧框架具有统计受限等距性质和统计不相干性质。结果，它们在恢复从通用随机信号模型获得的稀疏信号方面显示出接近最佳的理论保证。使用模拟，我们证明了构造的紧框架是恢复稀疏信号的良好候选者的有效性，相对于部分傅立叶矩阵，以及现有的非相干单位范式紧框架的构造。我们构造的非相干单元范数紧框架具有统计受限等距性质和统计不相干性质。结果，它们在恢复从通用随机信号模型获得的稀疏信号方面显示出接近最佳的理论保证。使用模拟，我们证明了构造的紧框架是恢复稀疏信号的良好候选者的有效性，相对于部分傅立叶矩阵，以及现有的非相干单位范式紧框架的构造。