This paper investigates the problem of stable signal estimation from undersampled, noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, a novel recovery guarantee for the ${\ell }^1$-analysis basis pursuit is derived, enabling accurate predictions of its sample complexity. The bounds on the number of required measurements explicitly depend on the Gram matrix of the analysis operator and therefore account for its mutual coherence structure. The presented results defy conventional wisdom which promotes the sparsity of analysis coefficients as the crucial quantity to be studied. In fact, this paradigm breaks down in many situations of interest, for instance, when applying a redundant (multilevel) frame as analysis prior. In contrast, the proposed sampling-rate bounds reliably capture the recovery capability of various practical examples. The proofs are based on establishing a sophisticated upper bound on the conic Gaussian mean width associated with the underlying ${\ell }^1$-analysis polytope.

本文研究了在稀疏模型的假设下，从欠采样，有噪声的亚高斯测量中获得稳定信号估计的问题。基于稀疏性的广义概念，为${\ell }^{\mathrm{1个}}$-推导了分析基础追踪，从而可以准确预测其样本复杂度。所需测量次数的界限明确取决于分析算子的Gram矩阵，因此考虑了其相互一致的结构。提出的结果违背了传统的观点，传统观点促进了稀疏的分析系数作为要研究的关键量。实际上，这种范例在许多感兴趣的情况下会崩溃，例如，在应用冗余（多级）框架作为先前的分析时。相反，建议的采样率范围可靠地捕获了各种实际示例的恢复能力。证明基于在与基础层相关的圆锥高斯平均宽度上建立复杂的上限${\ell }^{\mathrm{1个}}$分析多表位。