from torch import Tensor
from deepinv.physics.functional.multiplier import (
multiplier,
multiplier_adjoint,
)
from deepinv.physics.functional.convolution import conv2d, conv_transpose2d
import torch
[docs]
def product_convolution2d(
x: Tensor, w: Tensor, h: Tensor, padding: str = "valid"
) -> torch.Tensor:
r"""
Product-convolution operator in 2d. Details available in the following paper:
Escande, P., & Weiss, P. (2017).
`Approximation of integral operators using product-convolution expansions. <https://hal.science/hal-01301235/file/Approximation_Integral_Operators_Convolution-Product_Expansion_Escande_Weiss_2016.pdf>`_
Journal of Mathematical Imaging and Vision, 58, 333-348.
This forward operator performs
.. math::
y = \sum_{k=1}^K h_k \star (w_k \odot x)
where :math:`\star` is a convolution, :math:`\odot` is a Hadamard product, :math:`w_k` are multipliers :math:`h_k` are filters.
:param torch.Tensor x: Tensor of size (B, C, H, W)
:param torch.Tensor w: Tensor of size (b, c, K, H, W). b in {1, B} and c in {1, C}
:param torch.Tensor h: Tensor of size (b, c, K, h, w). b in {1, B} and c in {1, C}, h<=H and w<=W
:param padding: ( options = `valid`, `circular`, `replicate`, `reflect`. If `padding = 'valid'` the blurred output is smaller than the image (no padding), otherwise the blurred output has the same size as the image.
:return: torch.Tensor y
:rtype: tuple
"""
K = w.size(2)
result = 0.0
for k in range(K):
result += conv2d(
multiplier(x, w[:, :, k, ...]), h[:, :, k, ...], padding=padding
)
return result
def product_convolution2d_adjoint(
y: Tensor, w: Tensor, h: Tensor, padding: str = "valid"
) -> torch.Tensor:
r"""
Product-convolution adjoint operator in 2d.
:param torch.Tensor x: Tensor of size (B, C, ...)
:param torch.Tensor w: Tensor of size (b, c, K, ...)
:param torch.Tensor h: Tensor of size (b, c, K, ...)
:param padding: options = ``'valid'``, ``'circular'``, ``'replicate'``, ``'reflect'``.
If `padding = 'valid'` the blurred output is smaller than the image (no padding),
otherwise the blurred output has the same size as the image.
"""
K = w.size(2)
result = 0.0
for k in range(K):
result += multiplier_adjoint(
conv_transpose2d(y, h[:, :, k, ...], padding=padding), w[:, :, k, ...]
)
return result
