In order to detect small-scale deformations during disease propagation while allowing large-scale deformation needed for inter-subject registration, we wish to model deformation at multiple scales and represent the deformation at the relevant scales only. With the LDDMM registration framework, enforcing sparsity results in compact representations but with limited ability to represent deformation across scales. In contrast, the LDDKBM extension of LDDMM allows representations of deformation at multiple scales but it does not favour compactness and hence may represent deformation at more scales than necessary. In this paper, we combine a sparsity prior with the multi-scale framework resulting in an algorithm allowing compact representation of deformation across scales. We present a mathematical formulation of the algorithm and evaluate it on a dataset of annotated lung CT images.