Purpose: Magnetic resonance imaging systems usually feature linear and shift-invariant (stationary) transform characteristics. The point spread function or equivalently the modulation transfer function may thus be used for an objective quality assessment of imaging modalities. The recently introduced theory of compressed sensing, however, incorporates nonlinear and nonstationary reconstruction algorithms into the magnetic resonance imaging process which prohibits the usage of the classical point spread function and therefore the according evaluation. Methods: In this work, a local point spread function concept was applied to assess the quality of magnetic resonance images which were reconstructed by an iterative soft thresholding algorithm for compressed sensing. The width of the main lobe of the local point spread function was used to perform studies on the spatial and temporal resolution properties of both numerical phantom and in vivo images. The impact of k-space sampling patterns as well as additional sparsifying transforms on the local spatial image resolution was investigated. In addition, the local temporal resolution of image series, which were reconstructed by exploiting spatiotemporal sparsity, was determined. Finally, the dependency of the local resolution on the thresholding parameter of the algorithm was examined. Results: The sampling patterns as well as the additional sparsifying transform showed a distinct impact on the local image resolution of the phantom image. The reconstructions, which were using x-f-space as a sparse transform domain showed slight temporal blurring for dynamic parts of the imaged object. The local image resolution had a dependence on the thresholding parameter, which allowed for optimizing the reconstruction. Conclusions: Local point spread functions enable the evaluation of the local spatial and temporal resolution of images reconstructed with the nonlinear and nonstationary iterative soft thresholding algorithm. By determining the influence of thresholding parameter and sampling pattern chosen on this model-based reconstruction, the method allows selecting appropriate acquisition parameters and thus improving the results.