Suppose \(\mathbb{K}\) is either \(\mathbb{C}\) or \(\mathbb{R}\), \(x,y\in \mathbb{K}^N\), \(0\le s \[ (k-s)x_k^*\le \lVert x-y\rVert_1+\sigma_s(x)_1, \]

where \(x_k^*\) is the \(k\)-th component of the non-increasing rearrangement of \(x\) and \(\sigma_s(x)_1\) is its s-term approximation error [1, Lemma 1.14].

References Link to heading

1. I. Veselic. Class Lecture, Topic: Compressive Sensing. Technische Universität Dortmund, 2017.