low rank approximation has been extensively studied in the past. it is most suitable to reproduce rectangular like structures in the data. in this talk i introduce a generalization using ``shifted'' rank-1 matrices to approximate $a\in\mathbb{c}^{m\times n}$. these matrices are of the form $s_{\lambda}(uv^*)$ where $u\in\mathbb{c}^m$, $v\in\mathbb{c}^n$ and $\lambda\in\mathbb{z}^n$. the operator $s_{\lambda}$ circularly shifts the $k$-th column of $uv^*$ by $\lambda_k$. these kind of shifts naturally appear in applications, where an object $u$ is observed in $n$ measurements at different positions indicated by the shift $\lambda$. the vector $v$ gives the observation intensity. this model holds e.g., for seismic waves that are recorded at $n$ sensors at different times $\lambda$. the main difficulty of the above stated problem lies in finding a suitable shift vector $\lambda$. once the shift is known, a simple singular value decomposition can be applied to reconstruct $u$ and $v$. we propose a greedy method to reconstruct $\lambda$ and validate our approach in numerical examples. reference: f. boss mann, j. ma, enhanced image approximation using shifted rank-1 reconstruction, inverse problems and imaging, accepted 2019, https://arxiv.org/abs/1810.01681