International audienceThe Very Large Telescope instrument SPHERE is equipped with an integral field spectrograph. The sensor field is composed of thousands of spectra produced by a hexagonal lenslet array. We propose a new data reduction algorithm based on an inverse problem approach whose data fidelity is enforced by robust penalization to automatically identify the defective pixels. Our reconstructions by inversion of the forward model represent a notable improvement with respect to reconstructions obtained with the current data reduction pipeline (reconstructions based on data interpolation)