# RadioInterferometry

### *class* deepinv.physics.RadioInterferometry(img_size, samples_loc, dataWeight=None, k_oversampling=2, interp_points=7, real_projection=True, device='cpu', \*\*kwargs)

Bases: [`LinearPhysics`](https://deepinv.org/api/stubs/deepinv.physics.LinearPhysics.html.md#deepinv.physics.LinearPhysics)

Radio Interferometry measurement operator.

The operator handles ungridded measurements using the non-uniform FFT (NUFFT), which is based in Kaiser-Bessel
kernel interpolation. This particular implementation relies on the [torchkbnufft](https://github.com/mmuckley/torchkbnufft) package.

The forward operator is defined as $A:x \mapsto y$,
where $A$ can be decomposed as $A = GFZ \in \mathbb{C}^{m \times n}$.
There, $G \in \mathbb{C}^{m \times d}$ is a sparse interpolation matrix,
encoding the non-uniform Fourier transform,
$F \in \mathbb{C}^{d\times d}$ is the 2D Discrete orthonormal Fourier Transform,
$Z \in \mathbb{R}^{d\times n}$ is a zero-padding operator,
incorporating the correction for the convolution performed through the operator $G$.

* **Parameters:**
  * **img_size** ([*tuple*](https://docs.python.org/3.12/library/stdtypes.html#tuple)) – Size of the target image, e.g., (H, W).
  * **samples_loc** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Normalized sampling locations in the Fourier domain (Size: N x 2).
  * **dataWeight** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Data weighting for the measurements (Size: N). Default is `torch.tensor([1.0])` (i.e. no weighting).
  * **interp_points** (*Union* *[*[*int*](https://docs.python.org/3.12/library/functions.html#int) *,* *Sequence* *[*[*int*](https://docs.python.org/3.12/library/functions.html#int) *]* *]*) – Number of neighbors to use for interpolation in each dimension. Default is `7`.
  * **k_oversampling** ([*float*](https://docs.python.org/3.12/library/functions.html#float)) – Oversampling of the k space grid, should be between `1.25` and `2`. Default is `2`.
  * **real_projection** ([*bool*](https://docs.python.org/3.12/library/functions.html#bool)) – Apply real projection after the adjoint NUFFT. Default is `True`.
  * **device** ([*torch.device*](https://docs.pytorch.org/docs/stable/tensor_attributes.html#torch.device)) – Device where the operator is computed. Default is `cpu`.

#### WARNING
If the `real_projection` parameter is set to `False`, the output of the adjoint will have a complex type rather than a real typed.

#### NOTE
This class requires the `torchkbnufft` package to be installed. Install with `pip install torchkbnufft`.

#### A(x, \*\*kwargs)

Applies the weighted NUFFT operator to the input image.

* **Parameters:**
  **x** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input image
* **Returns:**
  ([`torch.Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) containing the measurements
* **Return type:**
  [*Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)

#### A_adjoint(y, \*\*kwargs)

Applies the adjoint of the weighted NUFFT operator.

* **Parameters:**
  **y** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input measurements
* **Returns:**
  ([`torch.Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) containing the reconstructed image
* **Return type:**
  [*Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)

<a id="sphx-glr-backref-deepinv-physics-radiointerferometry"></a>

## Examples using `RadioInterferometry`:

<div class="sphx-glr-thumbnails">
<!-- thumbnail-parent-div-open --><div class="sphx-glr-thumbcontainer" tooltip="In this example, we investigate a simple 2D Radio Interferometry (RI) imaging task with deepinverse. The following example and data are taken from aghabiglou2024r2d2. If you are interested in RI imaging problem and would like to see more examples or try the state-of-the-art algorithms, please check BASPLib.">![](auto_examples/external-libraries/images/thumb/sphx_glr_demo_ri_basic_thumb.png)

[Radio interferometric imaging with deepinverse](https://deepinv.org/auto_examples/external-libraries/demo_ri_basic.html.md)

  <div class="sphx-glr-thumbnail-title">Radio interferometric imaging with deepinverse</div>
</div>
<!-- thumbnail-parent-div-close --></div>