A general approach for multidimensional smoothing

Smoothing is closely related to regression in statistics. It is frequently applied to data that contain statistical noise in attempts to discern and highlight patterns concealed in the data. In medical imaging applications, the acquired data are often N dimensional (where N ⩾ 2 ) and thus multidimensional smoothing approaches would best exploit the multidimensional correlations inherent in the data. Unfortunately, extensions of advanced (especially adaptive) one‐dimensional smoothing approaches to multidimensional data are, in general, theoretically challenging and computationally prohibitive. In this work, we propose a novel approach that accomplishes effectively higher‐dimensional smoothing by exploiting the Fourier transform properties of the data to reduce data dimensions, allowing for lower‐dimensional smoothing. We present the theoretical basis for this approach and verify this approach by applying it to computer‐simulated data as well as real data acquired in medical imaging studies.