F p (x p,i ) is then given by: F p (x p,i ) := {f I×J (x p,i ) | ∀I ∈ T 0 z , ∀J ∈ T 0 t }, which is the collection of all coefficients f I×J (x p,i ) resulting from applying all possible filters g I×J to x p,i . F p (x p,i ) can be viewed as extending the coordinates of x p,i by computing averages based on the partition trees over the other two tensor axes of physical space z and of time t. Therefore, the value of the coefficient f I×J (x p,i ) ∈ F p (x p,i ) can be viewed as a non-local average at x pi evaluated by a low-pass filter, constructed based on the bi-folder I × J and the co-dependencies of the space z and time t.