Loss Functions

Similar to activation functions, two general types of loss functions have similar forms to Type-A and Type-B activations, operating on the real and imaginary or magnitude and phase, respectively.

class complextorch.nn.modules.loss.CVCauchyError(c: float = 1)

Complex-Valued Cauchy Error Function CVCauchyError.

\[\mathcal{L}(\mathbf{x}, \mathbf{y}) = \frac{1}{2}\text{sum}( c^2 / 2 \ln(1 + |\mathbf{x} - \mathbf{y}|^2/c^2) )\]

where \(c\) is typically set to unity.

Based on work from the following paper:

Ronny Hänsch. Complex-valued multi-layer perceptrons - an application to polarimetric SAR data

forward(x: CVTensor, y: CVTensor) → Tensor

Computes the complex-valued Cauchy error function.

Parameters:
Returns:

\(\frac{1}{2}\text{sum}( c^2 / 2 \ln(1 + |\mathbf{x} - \mathbf{y}|^2/c^2) )\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.CVFourthPowError

Complex Fourth Power Error Function

\[\mathcal{L}(\mathbf{x}, \mathbf{y}) = \frac{1}{2}\text{sum}(|\mathbf{x} - \mathbf{y}|^4)\]

Based on work from the following paper:

Ronny Hänsch. Complex-valued multi-layer perceptrons - an application to polarimetric SAR data

forward(x: CVTensor, y: CVTensor) → Tensor

Computes the complex-valued fourth power error function.

Parameters:
Returns:

\(\frac{1}{2}\text{sum}(|\mathbf{x} - \mathbf{y}|^4)\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.CVLogCoshError

Complex-Valued Log-Cosh Error Function CVLogCoshError.

\[\mathcal{L}(\mathbf{x}, \mathbf{y}) = \text{sum}(\ln(\cosh(|\mathbf{x} - \mathbf{y}|^2))\]

Based on work from the following paper:

Ronny Hänsch. Complex-valued multi-layer perceptrons - an application to polarimetric SAR data

forward(x: CVTensor, y: CVTensor) → Tensor

Computes the complex-valued log-cosh error function.

Parameters:
Returns:

\(\text{sum}(\ln(\cosh(|\mathbf{x} - \mathbf{y}|^2))\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.CVLogError

Complex-Valued Log Error Function CVLogError.

\[\mathcal{L}(\mathbf{x}, \mathbf{y}) = \text{sum}(|\ln(\mathbf{x}) - \ln(\mathbf{y})|^2)\]

Based on work from the following paper:

J Bassey, L Qian, X Li. A Survey of Complex-Valued Neural Networks

forward(x: CVTensor, y: CVTensor) → Tensor

Computes the complex-valued log error function.

Parameters:
Returns:

\(\text{sum}(|\ln(\mathbf{x}) - \ln(\mathbf{y})|^2)\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.CVQuadError

Complex-Valued Quadratic Error Function

\[\mathcal{L}(\mathbf{x}, \mathbf{y}) = \frac{1}{2}\text{sum}(|\mathbf{x} - \mathbf{y}|^2)\]

Based on work from the following paper:

Ronny Hänsch. Complex-valued multi-layer perceptrons - an application to polarimetric SAR data

forward(x: CVTensor, y: CVTensor) → Tensor

Computes the complex-valued quadratic error function.

Parameters:
Returns:

\(\frac{1}{2}\text{sum}(|\mathbf{x} - \mathbf{y}|^2)\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.GeneralizedSplitLoss(loss_r: Module, loss_i: Module)

Generalized Split Loss Function

Operates on the real and imaginary parts separately and sums the losses using the operation:

\[\mathcal{L}(\mathbf{x}, \mathbf{y}) = \mathcal{L}_\mathbb{R}(\mathbf{x}_\mathbb{R}, \mathbf{y}_\mathbb{R}) + \mathcal{L}_\mathbb{I}(\mathbf{x}_\mathbb{I}, \mathbf{y}_\mathbb{I})\]
forward(x: CVTensor, y: CVTensor) → Tensor

Computes the real/imag split loss function.

Parameters:
Returns:

\(\mathcal{L}_\mathbb{R}(\mathbf{x}_\mathbb{R}, \mathbf{y}_\mathbb{R}) + \mathcal{L}_\mathbb{I}(\mathbf{x}_\mathbb{I}, \mathbf{y}_\mathbb{I})\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.PerpLossSSIM

Perpendicular SSIM Loss Function

Based on work from the following paper:

M. L. Terpstra, M. Maspero, A. Sbrizzi, C. van den Berg. ⊥-loss: A symmetric loss function for magnetic resonance imaging reconstruction and image registration with deep learning.

forward(x: CVTensor, y: CVTensor) → Tensor

Computes perpendicular SSIM loss function.

Parameters:
Returns:

\(\texttt{PerpLossSSIM}(\mathbf{x}, \mathbf{y})\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.SSIM(win_size: int = 7, k1: float = 0.01, k2: float = 0.03)

Traditional Real-Valued SSIM Loss Function

Code modified from: https://gitlab.com/computational-imaging-lab/perp_loss

forward(x: Tensor, y: Tensor, data_range: Tensor | None = None, full: bool = False) → Tensor

Computes the SSIM metric on the real-valued tensors.

Parameters:

  • x (torch.Tensor) – estimated labels

  • y (torch.Tensor) – target/ground truth labels

  • data_range (Optional[torch.Tensor], optional) – Optional data range (max value of data, e.g., 255). Defaults to None.

  • full (bool, optional) – Compute full SSIM. Defaults to False.

Returns:

\(\texttt{SSIM}(\mathbf{x}, \mathbf{y})\)

Return type:

torch.Tensor

class complextorch.nn.modules.loss.SplitL1

Split L1 Loss Function

\[L1(\mathbf{x}, \mathbf{y}) = \texttt{L1}(\mathbf{x}_\mathbb{R}, \mathbf{y}_\mathbb{R}) + \texttt{L1}(\mathbf{x}_\mathbb{I}, \mathbf{y}_\mathbb{I})\]
class complextorch.nn.modules.loss.SplitMSE

Split MSE Loss Function

\[MSE(\mathbf{x}, \mathbf{y}) = \texttt{MSE}(\mathbf{x}_\mathbb{R}, \mathbf{y}_\mathbb{R}) + \texttt{MSE}(\mathbf{x}_\mathbb{I}, \mathbf{y}_\mathbb{I})\]
class complextorch.nn.modules.loss.SplitSSIM(win_size: int = 7, k1: float = 0.01, k2: float = 0.03)

Split SSIM Loss Function

Returns sum of SSIM over real and imaginary parts separately.

forward(x: CVTensor, y: CVTensor, data_range: Tensor | None = None, full: bool = False) → Tensor

Computes the real/imag split loss function.

Parameters:
Returns:

\(\mathcal{L}_\mathbb{R}(\mathbf{x}_\mathbb{R}, \mathbf{y}_\mathbb{R}) + \mathcal{L}_\mathbb{I}(\mathbf{x}_\mathbb{I}, \mathbf{y}_\mathbb{I})\)

Return type:

torch.Tensor