In this talk we will discuss various aniosotropic PDEs methods for applications to image processing. We will then discuss integro-differential equations inspired from (BV, L^2) and (BV, L^1) 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.