Whether in medical imaging, astronomy or remote sensing, the data are increasingly complex. In addition to the spatial dimension, the data may contain temporal or spectral information that characterises the different sources present in the image. The compromise between spatial resolution and temporal/spectral resolution is often at the expense of spatial resolution, resulting in a potentially large mixing of sources in the same pixel/voxel. Source separation methods must incorporate spatial information to estimate the contribution and signature of each source in the image. We consider the particular case where the position of the sources is approximately known thanks to external information that may come from another imaging modality or from a priori knowledge. We propose a spatially constrained dictionary learning source separation algorithm that uses e.g. high resolution segmentation map or regions of interest defined by an expert to regularise the source contribution estimation. The originality of the proposed model is the replacement of the sparsity constraint classically expressed in the form of an $\ell _{1}$ penalty on the localisation of sources by an indicator function exploiting the external source localisation information. The model is easily adaptable to different applications by adding or modifying the constraints on the sources properties in the optimisation problem. The performance of this algorithm has been validated on synthetic and quasi-real data, before being applied to real data previously analysed by other methods of the literature in order to compare the results. To illustrate the potential of the approach, different applications have been considered, from scintigraphic data to astronomy or fMRI data.

中文翻译：

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空间约束的在线词典学习，用于源分离

无论是在医学成像，天文学还是遥感领域，数据都越来越复杂。除了空间维度之外，数据还可以包含表征图像中存在的不同源的时间或光谱信息。空间分辨率和时间/光谱分辨率之间的折衷通常是以空间分辨率为代价的，从而导致在同一像素/体素中可能存在大量的源混合。源分离方法必须合并空间信息，以估计图像中每个源的贡献和特征。我们考虑这样一种特殊情况：由于外部信息可能来自其他成像方式或来自外部，因此可以大致了解光源的位置先验知识。我们提出了一种空间受限的字典学习源分离算法，该算法使用例如专家定义的高分辨率分割图或感兴趣区域，以规范源贡献估算。提出的模型的独创性是用稀疏约束替换了经典形式的稀疏约束。 $ \ ell _ {1} $ 通过利用外部源本地化信息的指示符功能对源的本地化进行惩罚。通过在优化问题中添加或修改对源属性的约束，该模型可以轻松适应不同的应用程序。该算法的性能已在合成和准真实数据上得到验证，然后再应用于先前通过其他文献方法分析过的真实数据以比较结果。为了说明该方法的潜力，已经考虑了从闪烁显像数据到天文学或fMRI数据的不同应用。