# conv3d_fft

### deepinv.physics.functional.conv3d_fft(x, filter, real_fft=True, padding='valid')

A helper function performing the 3d convolution of `x` and `filter` using FFT.

The adjoint of this operation is [`deepinv.physics.functional.conv_transpose3d_fft()`](https://deepinv.org/api/stubs/deepinv.physics.functional.conv_transpose3d_fft.html.md#deepinv.physics.functional.conv_transpose3d_fft).

If `b = 1` or `c = 1`, this function applies the same filter for each channel and each image.
Otherwise, each channel of each image is convolved with the corresponding kernel.

* **Parameters:**
  * **y** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Image of size `(B, C, D, H, W)`.
  * **filter** ([*torch.Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)) – Filter of size `(b, c, d, h, w)` where `b` can be either `1` or `B` and `c` can be either `1` or `C`.
  * **real_fft** ([*bool*](https://docs.python.org/3.12/library/functions.html#bool)) – for real filters and images choose `True` (default) to accelerate computation
  * **padding** ([*str*](https://docs.python.org/3.12/library/stdtypes.html#str)) – can be `'valid'`, `'circular'`, `'replicate'`, `'reflect'`,  `'constant'` or `'zeros'`.
    If `padding = 'valid'` the output is smaller than the image (no padding), otherwise the output has the same size as the image.
    Note that `'constant'` and `'zeros'` are equivalent.
    Default is `'valid'`.

#### NOTE
The filter center is located at `(d//2, h//2, w//2)`.

This function and [`deepinv.physics.functional.conv3d()`](https://deepinv.org/api/stubs/deepinv.physics.functional.conv3d.html.md#deepinv.physics.functional.conv3d) are equivalent. However, this function is more efficient for large filters but requires more memory.

* **Returns:**
  [`torch.Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor): the output of the convolution, which has the same shape as $x$ if `padding = 'circular'`, `(B, C, D-d+1, W-w+1, H-h+1)` otherwise.
* **Return type:**
  [*Tensor*](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor)