In this talk we will discuss various aniosotropic PDEs. We will then discuss integro-differential
equations inspired from (BV, L2) and (BV, L1) decompositions. Although the original motivation came from a variational approach, the resulting IDEs can be extended using standard techniques from PDE-based image processing. We use filtering, edge preserving and tangential smoothing to yield a family of modified IDE models with
applications to image denoising and image deblurring problems.