Blind Inverse Problems#
Following the notation of the library, here we consider measurements of the form \(y = \noise{\forw{x, \theta}}\), where \(\theta\) represents unknown physics parameters. Noise parameters associated to \(\noise{\cdot}\) may also be unknown. In this section, we consider two classes of problems:
Calibration problems: Estimate the unknown parameters \(\theta\) given paired signal and measurement data \((x,y)\)
Blind inverse problems: Jointly estimate the signal \(x\) and \(\theta\) parameters (and other noise parameters) from the measurements \(y\). Some methods directly estimate the signal without explicitly estimating the parameters.
Calibration problems#
If paired measurement and signal data is available at inference time, physics parameters can be estimated using optimization methods. See the example Calibrating physics operators for more details.
Physics parameters estimation#
If only measurement data is available \(\theta\) at inference time, we can estimate the parameters from the observed data, and then use any non-blind reconstructor to recover the image. The library provides the following parameter estimation models/algorithms:
Model/Algorithm |
Tensor Size (C, H, W) |
Pretrained Weights |
Physics |
Parameters estimated |
Examples |
|---|---|---|---|---|---|
C=3; H,W>8 |
RGB |
|
|||
C=2; H,W>64 |
(non-learned) |
|