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: 
If your image is modeled as an image which is noisy, blurry and heavily decimated the optimal thing to do is estimate the image given that model. 

The model is well defined in [@Laurent Duval](https://dsp.stackexchange.com/users/15892/laurent-duval)'s [answer](https://dsp.stackexchange.com/a/60605/128).  

I'd remark that in most real world cases the blurring is spatially variant hence it can't be modeled by convolution (Well, it is a generalized convolution).

In practice it is too hard (Was?) to solve such things and like in most cases we take the greedy approach: Step by Step.

Since most algorithms are SNR dependent, it makes sense first to handle the noise by Denoising. Pay attention that if we assume the image is blurred we have spatially correlated noise which is more tricky to deal with.

Then I'd handle the Super Resolution / Deblurring.  

Since those are closely related I'd certainly solve them in one step.  

Yet again, in case it is important to do them separately, start with Deblurring then Super Resolution.
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.
> 
> 
>