Subtle Inverse Crimes: Naïvely training machine learning algorithms could lead to overly-optimistic results

While open databases are an important resource in the Deep Learning (DL) era, they are sometimes used "off-label": data published for one task are used for training algorithms for a different one. This work aims to highlight that in some cases, this common practice may lead to biased, overly-optimistic results. We demonstrate this phenomenon for inverse problem solvers and show how their biased performance stems from hidden data preprocessing pipelines. We describe two preprocessing pipelines typical of open-access databases and study their effects on three well-established algorithms developed for Magnetic Resonance Imaging (MRI) reconstruction: Compressed Sensing (CS), Dictionary Learning (DictL), and DL. In this large-scale study we performed extensive computations. Our results demonstrate that the CS, DictL and DL algorithms yield systematically biased results when na\"ively trained on seemingly-appropriate data: the Normalized Root Mean Square Error (NRMSE) improves consistently with the preprocessing extent, showing an artificial increase of 25%-48% in some cases. Since this phenomenon is generally unknown, biased results are sometimes published as state-of-the-art; we refer to that as subtle inverse crimes. This work hence raises a red flag regarding na\"ive off-label usage of Big Data and reveals the vulnerability of modern inverse problem solvers to the resulting bias.