Tackling unsupervised source separation jointly with an additional inverse problem such as deconvolution is central for the analysis of multi-wavelength data. This becomes highly challenging when applied to large data sampled on the sphere such as those provided by wide-field observations in astrophysics, whose analysis requires the design of dedicated robust and yet effective algorithms. We therefore investigate a new joint deconvolution/sparse blind source separation method dedicated for data sampled on the sphere, coined SDecGMCA. It is based on a projected alternate least-squares minimization scheme, whose accuracy is proved to strongly rely on some regularization scheme in the present joint deconvolution/blind source separation setting. To this end, a regularization strategy is introduced that allows designing a new robust and effective algorithm, which is key to analyze large spherical data. Numerical experiments are carried out on toy examples and realistic astronomical data.

解决无监督信号源分离以及反卷积等反问题，对于分析多波长数据至关重要。当将其应用于在球体上采样的大数据（如天体物理学中的宽视场观测所提供的数据）时，这变得极具挑战性，而对它们的分析则需要设计专门的鲁棒而有效的算法。因此，我们研究了一种新的联合反卷积/稀疏盲源分离方法，该方法专用于在球体上采样的数据，即SDecGMCA。它基于一个投影的交替最小二乘最小化方案，在当前的联合反卷积/盲源分离设置中，其准确性被证明强烈依赖于某些正则化方案。为此，引入了一种正则化策略，该策略允许设计一种新的鲁棒且有效的算法，这对于分析大型球形数据非常关键。对玩具实例和真实的天文数据进行了数值实验。