 Sparse vector

A vector is s-sparse if it has at most $s$ nonzero coordinates. For $x\in {\mathbb{R}}^N$, its best s-term ${\ell }^1$ approximation error is ${\sigma }_s(x)={\min }_{z\text{ s-sparse}}\Vert x-z{\Vert }_1$, equal to the sum of the absolute values of the coordinates outside the largest $s$.