Need for adaptation: Adaptive block-size?

In regions where the image exhibits some uniform behaviour, a larger block-size corresponds to a lower MASE.
On the contrary, in the vicinity of edges, an increase in the block-size typically produces an increase in the MASE because of the less sparse representation of the signal.

A denoising algorithm based on 2D separable DCT with an adaptive block-size was proposed by Öktem et al. in 2001. The “classical” LPA-ICI was used to select the adaptive block-size in a pointwise manner.

( ktem, H., V. Katkovnik, K. Egiazarian, and J. Astola, “Local adaptive transform based image de-noising with varying window size”, Proc. IEEE Int. Conf. Image Process., ICIP 2001, Thessaloniki, Greece, pp. 273-276, Oct. 2001 )

However, edges can appear at any orientation and complex geometries in the image can impose strong limitations on the adaptivity based on square blocks.
Clearly, an improved approach should go beyond the traditional block DCT, in order to better adapt to the various arbitrarily oriented structures that may be present in the image.