Good filtering: Seeking a low MASE

In order to achieve a low MASE, one would like that
the thresholded coefficients would be as small as possible (low bias), while
the non-thresholded coefficients as few as possible (low variance).

In other words, we look for a sparse, compact representation of the signal.

Because of its energy-compaction efficiency, the 2D separable DCT is the most frequently used transforms in image processing.
However, it is well known that in the presence of sharp discontinuities (i.e. edges) the DCT, together with all other oscillatory transforms, is unable to provide a sparse representation of the signal.

Fixed-size square blocks are far from being an ideal choice.