Modification of the SVD unfolding regularization method

Unfolding is currently an important stage of processing experimental data, reducing the effect of errors and reconstructing approximately real distributions of quantities. Numerous approaches exist to solve this problem; in particular, they are widely used in the modern physics of atomic nuclei and elementary particles, space physics, and other related areas. However, many algorithms are not designed or are poorly adapted to reconstruct multidimensional distributions corresponding to, e.g., several characteristics of particles measured simultaneously. In this work, a method has been proposed to adapt the singular value decomposition (SVD) unfolding algorithm to the multidimensional case. The proposed modified method has been tested in application to simulation data for the cosmic ray spectrum measured in the PAMELA space experiment. This method not only makes it possible to estimate the real distribution of a multidimensional quantity (momentum and two angles specifying the direction of entering a particle into an instrument) but also provides a better result compared to the classical SVD approach in the one-dimensional case (only the momentum of the particle).