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losses

Data losses definitions.

Classes:

  • LossCCF –

    Custom convolutional filter decomposition loss function.

  • LossDWTN –

    Multi-level n-dimensional discrete wavelet transform loss function.

  • LossRegularizer –

    Base class for the regularizer losses.

  • LossSWTN –

    Multi-level n-dimensional stationary wavelet transform loss function.

  • LossTGV –

    Total Generalized Variation loss function.

  • LossTV –

    Total Variation loss function.

LossCCF 

LossCCF(
    lambda_val: float,
    filters: Tensor,
    weights: Tensor,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    min_approx: bool = False,
)

Bases: LossRegularizer

Custom convolutional filter decomposition loss function.

Methods:

  • forward –

    Compute decomposition on current batch.

Source code in src/autoden/losses.py 
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def __init__(
    self,
    lambda_val: float,
    filters: pt.Tensor,
    weights: pt.Tensor,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    min_approx: bool = False,
) -> None:
    super().__init__(size_average, reduce, reduction)
    self.lambda_val = lambda_val
    self.filters = filters
    self.weights = weights
    self.min_approx = min_approx

    self.n_dims = filters.ndim - 2

    if filters.shape[0] != weights.numel():
        raise ValueError(
            f"The number of convolution kernels ({filters.shape[0]}) does"
            f" not match the number of weights ({weights.numel()})"
        )

    self.weights = weights.reshape([1, -1, *(1,) * self.n_dims])

forward 

forward(img: Tensor) -> Tensor

Compute decomposition on current batch.

Source code in src/autoden/losses.py 
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def forward(self, img: pt.Tensor) -> pt.Tensor:
    """Compute decomposition on current batch."""
    _check_input_tensor(img, self.n_dims)
    axes = list(range(-(self.n_dims + 1), 0))

    decomp = CustomFilterDecomposition(kernels=self.filters[not self.min_approx :, ...], device=img.device)
    weights = self.weights[:, not self.min_approx :, ...].to(img.device)

    coeffs = decomp.analyze(img)

    loss_vals: pt.Tensor = self.lambda_val * (weights * coeffs).abs().sum(1).sum(axes)

    if self.reduction.lower() == "mean":
        return loss_vals.mean()
    elif self.reduction.lower() == "sum":
        return loss_vals.sum()
    else:
        return loss_vals

LossDWTN 

LossDWTN(
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = False,
    wavelet: str = "haar",
    level: int = 2,
    n_dims: int = 2,
    min_approx: bool = True,
    lvl_scale: bool = False,
)

Bases: LossRegularizer

Multi-level n-dimensional discrete wavelet transform loss function.

Methods:

  • forward –

    Compute wavelet decomposition on current batch.

Source code in src/autoden/losses.py 
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def __init__(
    self,
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = False,
    wavelet: str = "haar",
    level: int = 2,
    n_dims: int = 2,
    min_approx: bool = True,
    lvl_scale: bool = False,
) -> None:
    super().__init__(size_average, reduce, reduction)
    self.wavelet = wavelet
    self.lambda_val = lambda_val
    self.isotropic = isotropic
    self.level = level
    self.n_dims = n_dims
    self.min_approx = min_approx
    self.lvl_scale = lvl_scale

forward 

forward(img: Tensor) -> Tensor

Compute wavelet decomposition on current batch.

Source code in src/autoden/losses.py 
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def forward(self, img: pt.Tensor) -> pt.Tensor:
    """Compute wavelet decomposition on current batch."""
    _check_input_tensor(img, self.n_dims)
    axes = list(range(-(self.n_dims + 1), 0))

    coeffs = dwtn(img, wavelet=self.wavelet, level=self.level, axes=axes, mode="constant")
    wl_norm = wavelet_norm(self.wavelet, level=self.level, ndims=self.n_dims, device=img.device, dtype=img.dtype)

    if self.min_approx:
        wl_val = [coeffs[0].abs().sum(axes)]
    else:
        wl_val = []

    for ii_lvl, lvl_c in enumerate(coeffs[1:]):
        coeff = pt.stack([c for _, c in lvl_c.items()], dim=0)

        if self.isotropic:
            wl_lvl_val = coeff.sum(dim=0).abs().sum(axes)
        else:
            wl_lvl_val = coeff.abs().sum(dim=0).sum(axes)

        if self.lvl_scale:
            wl_lvl_val = wl_lvl_val / wl_norm[ii_lvl]
        wl_val.append(wl_lvl_val)

    loss_vals: pt.Tensor = self.lambda_val * pt.stack(wl_val, dim=0).sum(dim=0) / ((self.level + self.min_approx) ** 0.5)

    if self.reduction.lower() == "mean":
        return loss_vals.mean()
    elif self.reduction.lower() == "sum":
        return loss_vals.sum()
    else:
        return loss_vals

LossRegularizer

Bases: _Loss

Base class for the regularizer losses.

Methods:

  • forward –

    Abstract forward method for regularizer losses.

forward abstractmethod 

forward(img: Tensor) -> Tensor

Abstract forward method for regularizer losses.

Parameters:

  • img (Tensor) –

    The expected input signal

Returns:

  • Tensor –

    The returned loss value

Source code in src/autoden/losses.py 
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@abstractmethod
def forward(self, img: pt.Tensor) -> pt.Tensor:
    """Abstract forward method for regularizer losses.

    Parameters
    ----------
    img : pt.Tensor
        The expected input signal

    Returns
    -------
    pt.Tensor
        The returned loss value
    """

LossSWTN 

LossSWTN(
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = False,
    wavelet: str = "haar",
    level: int = 2,
    n_dims: int = 2,
    min_approx: bool = True,
    lvl_scale: bool = True,
)

Bases: LossRegularizer

Multi-level n-dimensional stationary wavelet transform loss function.

Methods:

  • forward –

    Compute wavelet decomposition on current batch.

Source code in src/autoden/losses.py 
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def __init__(
    self,
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = False,
    wavelet: str = "haar",
    level: int = 2,
    n_dims: int = 2,
    min_approx: bool = True,
    lvl_scale: bool = True,
) -> None:
    super().__init__(size_average, reduce, reduction)
    self.wavelet = wavelet
    self.lambda_val = lambda_val
    self.isotropic = isotropic
    self.level = level
    self.n_dims = n_dims
    self.min_approx = min_approx
    self.lvl_scale = lvl_scale

forward 

forward(img: Tensor) -> Tensor

Compute wavelet decomposition on current batch.

Source code in src/autoden/losses.py 
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def forward(self, img: pt.Tensor) -> pt.Tensor:
    """Compute wavelet decomposition on current batch."""
    _check_input_tensor(img, self.n_dims)
    axes = list(range(-(self.n_dims + 1), 0))

    coeffs = swtn(img, wavelet=self.wavelet, level=self.level, axes=axes, mode="constant")
    wl_norm = wavelet_norm(self.wavelet, level=self.level, ndims=self.n_dims, device=img.device, dtype=img.dtype)

    if self.min_approx:
        wl_val = [coeffs[0].abs().sum(axes)]
    else:
        wl_val = []

    for ii_lvl, lvl_c in enumerate(coeffs[1:]):
        coeff = pt.stack([c for _, c in lvl_c.items()], dim=0)

        if self.isotropic:
            wl_lvl_val = coeff.sum(dim=0).abs().sum(axes)
        else:
            wl_lvl_val = coeff.abs().sum(dim=0).sum(axes)

        if self.lvl_scale:
            wl_lvl_val = wl_lvl_val / wl_norm[ii_lvl]
        wl_val.append(wl_lvl_val)

    loss_vals: pt.Tensor = self.lambda_val * pt.stack(wl_val, dim=0).sum(dim=0) / ((self.level + self.min_approx) ** 0.5)

    if self.reduction.lower() == "mean":
        return loss_vals.mean()
    elif self.reduction.lower() == "sum":
        return loss_vals.sum()
    else:
        return loss_vals

LossTGV 

LossTGV(
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = True,
    n_dims: int = 2,
)

Bases: LossTV

Total Generalized Variation loss function.

Methods:

  • forward –

    Compute total variation statistics on current batch.

Source code in src/autoden/losses.py 
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def __init__(
    self,
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = True,
    n_dims: int = 2,
) -> None:
    super().__init__(size_average, reduce, reduction)
    self.lambda_val = lambda_val
    self.isotropic = isotropic
    self.n_dims = n_dims

forward 

forward(img: Tensor) -> Tensor

Compute total variation statistics on current batch.

Source code in src/autoden/losses.py 
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def forward(self, img: pt.Tensor) -> pt.Tensor:
    """Compute total variation statistics on current batch."""
    _check_input_tensor(img, self.n_dims)
    axes = list(range(-(self.n_dims + 1), 0))

    diffs = [_differentiate(img, dim=dim, position="post") for dim in range(-self.n_dims, 0)]
    diffdiffs = [_differentiate(d, dim=dim, position="pre") for dim in range(-self.n_dims, 0) for d in diffs]

    if self.isotropic:
        tv_val = pt.sqrt(pt.stack([pt.pow(d, 2) for d in diffs], dim=0).sum(dim=0))
        jac_val = pt.sqrt(pt.stack([pt.pow(d, 2) for d in diffdiffs], dim=0).sum(dim=0))
    else:
        tv_val = pt.stack([d.abs() for d in diffs], dim=0).sum(dim=0)
        jac_val = pt.stack([d.abs() for d in diffdiffs], dim=0).sum(dim=0)

    loss_vals: pt.Tensor = self.lambda_val * (tv_val.sum(axes) + jac_val.sum(axes) / 4)

    if self.reduction.lower() == "mean":
        return loss_vals.mean()
    elif self.reduction.lower() == "sum":
        return loss_vals.sum()
    else:
        return loss_vals

LossTV 

LossTV(
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = True,
    n_dims: int = 2,
)

Bases: LossRegularizer

Total Variation loss function.

Methods:

  • forward –

    Compute total variation statistics on current batch.

Source code in src/autoden/losses.py 
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def __init__(
    self,
    lambda_val: float,
    size_average=None,
    reduce=None,
    reduction: str = "mean",
    isotropic: bool = True,
    n_dims: int = 2,
) -> None:
    super().__init__(size_average, reduce, reduction)
    self.lambda_val = lambda_val
    self.isotropic = isotropic
    self.n_dims = n_dims

forward 

forward(img: Tensor) -> Tensor

Compute total variation statistics on current batch.

Source code in src/autoden/losses.py 
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def forward(self, img: pt.Tensor) -> pt.Tensor:
    """Compute total variation statistics on current batch."""
    _check_input_tensor(img, self.n_dims)
    axes = list(range(-(self.n_dims + 1), 0))

    diffs = [_differentiate(img, dim=dim, position="post") for dim in range(-self.n_dims, 0)]
    diffs = pt.stack(diffs, dim=0)

    if self.isotropic:
        # tv_val = pt.sqrt(pt.stack([pt.pow(d, 2) for d in diffs], dim=0).sum(dim=0))
        tv_val = pt.sqrt(pt.pow(diffs, 2).sum(dim=0))
    else:
        # tv_val = pt.stack([d.abs() for d in diffs], dim=0).sum(dim=0)
        tv_val = diffs.abs().sum(dim=0)

    loss_vals: pt.Tensor = self.lambda_val * tv_val.sum(axes)

    if self.reduction.lower() == "mean":
        return loss_vals.mean()
    elif self.reduction.lower() == "sum":
        return loss_vals.sum()
    else:
        return loss_vals