Question: In the normal workflow of image processing, there are multiple operations, increase image contrast, image denoising, image deblur and image super-resolution. What are the sequence/order of performing these different operations. Are there any overlap among these operations?

Answer: 
Contrast, additive noise, (invariant) blurring and subsampling could be formulated together in a single optimization framework. This can theoretically be dealt with, provided that loss and penalty functions are tractable, in many fashions, globally or in an iterative fashion. So they overlap. A possible global model is:

$$y = D(\phi(h\ast x)+w)$$

with:

* $y$: observed signal
* $x$: initial discrete signal
* $h$: impulse response of the convolution or blurring filter
* $\phi$: non-linear contrast function (e.g. saturation)
* $w$: noise
* $D$: decimation

It is possible to start from the least linear to the most linear operation, as linear yields the easiest constrained/structured algorithms. For one recent global attempt, with sparse assumptions: [Sparse signal reconstruction for nonlinear models via piecewise rational optimization](https://doi.org/10.1016/j.sigpro.2020.107835):

> 
> We propose a method to reconstruct sparse signals degraded by a
> nonlinear distortion and acquired at a limited sampling rate. Our
> method formulates the reconstruction problem as a nonconvex
> minimization of the sum of a data fitting term and a penalization
> term. In contrast with most previous works which settle for
> approximated local solutions, we seek for a global solution to the
> obtained challenging nonconvex problem. Our global approach relies on
> the so-called Lasserre relaxation of polynomial optimization. We here
> specifically include in our approach the case of piecewise rational
> functions, which makes it possible to address a wide class of
> nonconvex exact and continuous relaxations of the l0 penalization
> function. Additionally, we study the complexity of the optimization
> problem. It is shown how to use the structure of the problem to
> lighten the computational burden efficiently. Finally, numerical
> simulations illustrate the benefits of our method in terms of both
> global optimality and signal reconstruction.
> 
> 
>
I suggest you take a look at this paper:  

*End-to-End Learning for Joint Image Demosaicing, Denoising and Super-Resolution*.  

in **Section 3. Proposed method**, they have discussed the execution order of image demosaicing, denoising, and super-resolution. From the paper,

> 
> For the mixture problem of image demosaicing, denoising and super-resolution, a clean high-resolution color image should be estimated from its noisy low-resolution raw image. For the execution order, **demosaicing
> should follow denoising**, like in [29], to avoid complications in filtering correlated noise after demosaicing. In addition, **the demosaicing should be performed before superresolution** because the correlation across color channels can be exploited when super-resolving color image. Besides
> this reason, performing super-resolution on raw image will
> destroy the original mosaic pattern, which increases the difficulty of demosaicing.
> 
> 
>