product_convolution2d

deepinv.physics.functional.product_convolution2d(x, w, h, padding='valid')

Product-convolution operator in 2d. Details available in the paper Escande and Weiss[1].

This forward operator performs

\[y = \sum_{k=1}^K h_k \star (w_k \odot x)\]

where \(\star\) is a convolution, \(\odot\) is a Hadamard product, \(w_k\) are multipliers \(h_k\) are filters.

Parameters:

• x (torch.Tensor) – Tensor of size (B, C, H, W)

• w (torch.Tensor) – Tensor of size (b, c, K, H, W). \(b \in \{1, B\}\) and \(c \in \{1, C\}\)

• h (torch.Tensor) – Tensor of size (b, c, K, h, w). \(b \in \{1, B\}\) and \(c \in \{1, C\}\), \(h\leq H\) and \(w\leq W\).

• padding (str) – ( 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.

Returns:

torch.Tensor y

Return type:

tuple

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References:

[1]

Paul Escande and Pierre Weiss. Approximation of integral operators using product-convolution expansions. Journal of Mathematical Imaging and Vision, 58:333–348, 2017.