Introduction

Reconstruction algorithms define an inversion function \(\hat{x}=\inversef{y}{A}\) which attempts to recover a signal \(x\) from measurements \(y\), (possibly) given an operator \(A\). All reconstruction algorithms in the library inherit from the deepinv.models.Reconstructor base class.

Below we provide a summary of existing reconstruction methods, and a qualitative description of their reconstruction performance and speed.

Tip

Some methods do not require any training and can be quickly deployed in your problem.

Tip

If you need to train your model and don’t have ground truth data, the library provides a large set of self-supervised losses which can learn from measurement data alone.

Table 4 Reconstruction methods

Family of methods	Description	Requires Training	Iterative	Sampling
Artifact Removal	Applies a neural network to a non-learned pseudo-inverse	Yes	No	No
Plug-and-Play (PnP)	Leverages pretrained denoisers as priors within an optimisation algorithm.	No	Yes	No
Unfolded Networks	Constructs a trainable architecture by unrolling a PnP algorithm.	Yes	Only DEQ	No
Diffusion	Leverages pretrained denoisers within a ODE/SDE.	No	Yes	Yes
Non-learned priors	Solves an optimization problem with hand-crafted priors.	No	Yes	No
Markov Chain Monte Carlo	Leverages pretrained denoisers as priors within an optimisation algorithm.	No	Yes	Yes
Unconditional GANs, deep image prior	Uses a generator network to model the set of possible images.	No	Yes	Depends

Note

Some algorithms might be better at reconstructing images with good perceptual quality (e.g. diffusion methods) whereas other methods are better at reconstructing images with low distortion (close to the ground truth).