# Blind Inverse Problems Following the [notation of the library](https://deepinv.org/user_guide/physics/intro.html.md#parameter-dependent-operators), 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](https://deepinv.org/auto_examples/blind-inverse-problems/demo_optimizing_physics_parameter.html.md#sphx-glr-auto-examples-blind-inverse-problems-demo-optimizing-physics-parameter-py) 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: #### Identification models | Model/Algorithm | Tensor Size (C, H, W) | Pretrained Weights | Physics | Parameters estimated | Examples | |-------------------------------------------------------------------------------------------------------------------------|-------------------------|----------------------|----------------------------------------------------------------------------------------------------|---------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------| | [`KernelIdentificationNetwork`](https://deepinv.org/api/stubs/deepinv.models.KernelIdentificationNetwork.html.md#deepinv.models.KernelIdentificationNetwork) | C=3; H,W>8 | RGB | [`SpaceVaryingBlur`](https://deepinv.org/api/stubs/deepinv.physics.SpaceVaryingBlur.html.md#deepinv.physics.SpaceVaryingBlur) | `filters`, `multipliers` | [blind deblurring](https://deepinv.org/auto_examples/blind-inverse-problems/demo_blind_deblurring.html.md#sphx-glr-auto-examples-blind-inverse-problems-demo-blind-deblurring-py). | | [`ESPIRiT`](https://deepinv.org/api/stubs/deepinv.physics.MultiCoilMRI.html.md#deepinv.physics.MultiCoilMRI) | C=2; H,W>64 | (non-learned) | [`MultiCoilMRI`](https://deepinv.org/api/stubs/deepinv.physics.MultiCoilMRI.html.md#deepinv.physics.MultiCoilMRI) | `coil_maps` | [MRI coil map estimation](https://deepinv.org/auto_examples/physics/demo_mri_tour.html.md#sphx-glr-auto-examples-physics-demo-mri-tour-py). | | [`WaveletNoiseEstimator`](https://deepinv.org/api/stubs/deepinv.models.WaveletNoiseEstimator.html.md#deepinv.models.WaveletNoiseEstimator) | C=1, 2, 3 | (non-learned) | [`GaussianNoise`](https://deepinv.org/api/stubs/deepinv.physics.GaussianNoise.html.md#deepinv.physics.GaussianNoise) | `sigma` | [noise level estimation](https://deepinv.org/auto_examples/blind-inverse-problems/demo_blind_denoising.html.md#sphx-glr-auto-examples-blind-inverse-problems-demo-blind-denoising-py). | | [`Patch`](https://deepinv.org/api/stubs/deepinv.models.PatchCovarianceNoiseEstimator.html.md#deepinv.models.PatchCovarianceNoiseEstimator) | C=1, 2, 3 | (non-learned) | [`GaussianNoise`](https://deepinv.org/api/stubs/deepinv.physics.GaussianNoise.html.md#deepinv.physics.GaussianNoise) | `sigma` | [noise level estimation](https://deepinv.org/auto_examples/blind-inverse-problems/demo_blind_denoising.html.md#sphx-glr-auto-examples-blind-inverse-problems-demo-blind-denoising-py). | | [`Blind Richardson-Lucy`](https://deepinv.org/api/stubs/deepinv.optim.BlindRL.html.md#deepinv.optim.BlindRL) | C>=1; H,W arbitrary | (non-learned) | [`Blur`](https://deepinv.org/api/stubs/deepinv.physics.Blur.html.md#deepinv.physics.Blur) with circular padding | clean image `x`, blur kernel `filter` | [blind Richardson-Lucy](https://deepinv.org/auto_examples/blind-inverse-problems/demo_blind_richardsonlucy.html.md#sphx-glr-auto-examples-blind-inverse-problems-demo-blind-richardsonlucy-py). |