product_convolution2d#

deepinv.physics.functional.product_convolution2d(x, w, h, padding='valid', use_fft=False, mask_first=True)[source]#

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

If mask_first=True (default), this forward operator performs

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

whereas if mask_first=False, the multipliers are applied after the convolutions, i.e.

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

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 \(c \in \{1, C\}\). If mask_first=False and padding='valid', the spatial size of the multipliers should match the size of the convolution output instead, i.e. \((b, c, K, H-h+1, W-w+1)\).

  • 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' or 'constant'). If padding = `'valid' the blurred output is smaller than the image (no padding), otherwise the blurred output has the same size as the image.

  • use_fft (bool) – whether to use FFT-based convolutions. If True, it uses FFT-based convolutions which can be faster for large kernels.

  • mask_first (bool) – whether the multipliers are applied before (True, default) or after (False) the convolutions.

Returns:

torch.Tensor the blurry image.

Return type:

Tensor

References: