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It is well known that the discrete cosine transform is a good transform to compress system matrices from magnetic particle imaging scanners that have a field-free point traveling along a Lissajous trajectory. With help of the compressed system matrix, the reconstruction of the particle distribution can be accelerated. However, the discrete cosine transform is a global transform along the spatial dimension of the system matrix. This has the disadvantage that no multiresolution analysis can be performed due to the loss of the spatial resolution. A typical strategy to implement a multiresolution analysis is to perform a discrete wavelet transform. Unfortunately, the discrete wavelet transform is not as sparsifying as the cosine transform for magnetic particle imaging system matrices. By combing the advantages of both transforms, we develop a strategy that gives rise to a multiresolution analysis with a similar performance as the discrete cosine transform at the full-resolution level, but with further resolution levels. We shortly discuss that the developed representation is a good starting point for advanced particle distribution reconstruction techniques that benefit from a multiresolution analysis.Int. J. Mag. Part. Imag. 4(2), 2018, Article ID: 1811002, DOI: 10.18416/IJMPI.2018.1811002