Noise Models

`GaussianMixtureNoiseModel`

Bases: Module

Define a noise model parameterized as a mixture of gaussians.

If config.path is not provided a new object is initialized from scratch. Otherwise, a model is loaded from config.path.

Parameters:

Name	Type	Description	Default
`config`	`GaussianMixtureNMConfig`	A `pydantic` model that defines the configuration of the GMM noise model.	required

Attributes:

Name	Type	Description
`min_signal`	`float`	Minimum signal intensity expected in the image.
`max_signal`	`float`	Maximum signal intensity expected in the image.
`path`	`Union[str, Path]`	Path to the directory where the trained noise model (*.npz) is saved in the `train` method.
`weight`	`Parameter`	A [3*n_gaussian, n_coeff] sized array containing the values of the weights describing the GMM noise model, with each row corresponding to one parameter of each gaussian, namely [mean, standard deviation and weight]. Specifically, rows are organized as follows: - first n_gaussian rows correspond to the means - next n_gaussian rows correspond to the weights - last n_gaussian rows correspond to the standard deviations If `weight=None`, the weight array is initialized using the `min_signal` and `max_signal` parameters.
`n_gaussian`	`int`	Number of gaussians in the mixture.
`n_coeff`	`int`	Number of coefficients to describe the functional relationship between gaussian parameters and the signal. 2 implies a linear relationship, 3 implies a quadratic relationship and so on.
`device`	`device`	GPU device.
`min_sigma`	`float`	All values of `standard deviation` below this are clamped to this value.

`fit(signal, observation, learning_rate=0.1, batch_size=250000, n_epochs=2000, lower_clip=0.0, upper_clip=100.0)`

Training to learn the noise model from signal - observation pairs.

Parameters:

Name	Type	Description	Default
`signal`	`NDArray`	Clean Signal Data	required
`observation`	`NDArray`	Noisy Observation Data	required
`learning_rate`	`float`	Learning rate. Default = 1e-1.	`0.1`
`batch_size`	`int`	Nini-batch size. Default = 250000.	`250000`
`n_epochs`	`int`	Number of epochs. Default = 2000.	`2000`
`lower_clip`	`int`	Lower percentile for clipping. Default is 0.	`0.0`
`upper_clip`	`int`	Upper percentile for clipping. Default is 100.	`100.0`

`get_gaussian_parameters(signals)`

Returns the noise model for given signals

Parameters:

Name	Type	Description	Default
`signals`	`Tensor`	Underlying signals	required

Returns:

Name	Type	Description
`noise_model`	`list of Tensor`	Contains a list of `mu`, `sigma` and `alpha` for the `signals`

`get_signal_observation_pairs(signal, observation, lower_clip, upper_clip)`

Returns the Signal-Observation pixel intensities as a two-column array

Parameters:

Name	Type	Description	Default
`signal`	`numpy array`	Clean Signal Data	required
`observation`	`NDArray`	Noisy observation Data	required
`lower_clip`	`float`	Lower percentile bound for clipping.	required
`upper_clip`	`float`	Upper percentile bound for clipping.	required

Returns:

Name	Type	Description
`noise_model`	`list of torch floats`	Contains a list of `mu`, `sigma` and `alpha` for the `signals`

`likelihood(observations, signals)`

Evaluates the likelihood of observations given the signals and the corresponding gaussian parameters.

Parameters:

Name	Type	Description	Default
`observations`	`Tensor`	Noisy observations. Shape is (batch, 1, dim1, dim2).	required
`signals`	`Tensor`	Underlying signals. Shape is (batch, 1, dim1, dim2).	required

Returns:

Name	Type	Description
`value`	`torch.Tensor:`	Likelihood of observations given the signals and the GMM noise model

`normal_density(x, mean, std)`

Evaluates the normal probability density at x given the mean mean and standard deviation std.

Parameters:

Name	Type	Description	Default
`x`	`Tensor`	The ground-truth tensor. Shape is (batch, 1, dim1, dim2).	required
`mean`	`Tensor`	The inferred mean of distribution. Shape is (batch, 1, dim1, dim2).	required
`std`	`Tensor`	The inferred standard deviation of distribution. Shape is (batch, 1, dim1, dim2).	required

Returns:

Name	Type	Description
`tmp`	`Tensor`	Normal probability density of `x` given `mean` and `std`

`polynomial_regressor(weight_params, signals)`

Combines weight_params and signal signals to regress for the gaussian parameter values.

Parameters:

Name	Type	Description	Default
`weight_params`	`Tensor`	Corresponds to specific rows of the `self.weight`	required
`signals`	`Tensor`	Signals	required

Returns:

Name	Type	Description
`value`	`Tensor`	Corresponds to either of mean, standard deviation or weight, evaluated at `signals`

`sample_observation_from_signal(signal)`

Sample an instance of observation based on an input signal using a learned Gaussian Mixture Model. For each pixel in the input signal, samples a corresponding noisy pixel.

Parameters:

Name	Type	Description	Default
`signal`	`NDArray`	Clean 2D signal data.	required

Returns:

Name	Type	Description
`observation`	`numpy array`	An instance of noisy observation data based on the input signal.

`save(path, name)`

Save the trained parameters on the noise model.

Parameters:

Name	Type	Description	Default
`path`	`str`	Path to save the trained parameters.	required
`name`	`str`	File name to save the trained parameters.	required

`MultiChannelNoiseModel`

Bases: Module

`likelihood(obs, signal)`

Compute the likelihood of observations given signals for each channel.

Parameters:

Name	Type	Description	Default
`obs`	`Tensor`	Noisy observations, i.e., the target(s). Specifically, the input noisy image for HDN, or the noisy unmixed images used for supervision for denoiSplit. Shape: (B, C, [Z], Y, X), where C is the number of unmixed channels.	required
`signal`	`Tensor`	Underlying signals, i.e., the (clean) output of the model. Specifically, the denoised image for HDN, or the unmixed images for denoiSplit. Shape: (B, C, [Z], Y, X), where C is the number of unmixed channels.	required

`create_histogram(bins, min_val, max_val, observation, signal)`

Creates a 2D histogram from 'observation' and 'signal'.

Parameters:

Name	Type	Description	Default
`bins`	`int`	Number of bins in x and y.	required
`min_val`	`float`	Lower bound of the lowest bin in x and y.	required
`max_val`	`float`	Upper bound of the highest bin in x and y.	required
`observation`	`ndarray`	3D numpy array (stack of 2D images). Observation.shape[0] must be divisible by signal.shape[0]. Assumes that n subsequent images in observation belong to one image in 'signal'.	required
`signal`	`ndarray`	3D numpy array (stack of 2D images).	required

Returns:

Name	Type	Description
`histogram`	`ndarray`	A 3D array: - histogram[0]: Normalized 2D counts. - histogram[1]: Lower boundaries of bins along y. - histogram[2]: Upper boundaries of bins along y.
	`The values for x can be obtained by transposing 'histogram[1]' and 'histogram[2]'.`

`multichannel_noise_model_factory(model_config)`

Multi-channel noise model factory.

Parameters:

Name	Type	Description	Default
`model_config`	`Optional[MultiChannelNMConfig]`	Noise model configuration, a `MultiChannelNMConfig` config that defines noise models for the different output channels.	required

Returns:

Type	Description
`Optional[MultiChannelNoiseModel]`	A noise model instance.

Raises:

Type	Description
`NotImplementedError`	If the chosen noise model `model_type` is not implemented. Currently only `GaussianMixtureNoiseModel` is implemented.

`noise_model_factory(model_config)`

Noise model factory for single-channel noise models.

Parameters:

Name	Type	Description	Default
`model_config`	`Optional[GaussianMixtureNMConfig]`	Noise model configuration for a single Gaussian mixture noise model.	required

Returns:

Type	Description
`Optional[GaussianMixtureNoiseModel]`	A single noise model instance, or None if no config is provided.

Raises:

Type	Description
`NotImplementedError`	If the chosen noise model `model_type` is not implemented. Currently only `GaussianMixtureNoiseModel` is implemented.

`train_gm_noise_model(model_config, signal, observation)`

Train a Gaussian mixture noise model.

Parameters:

Name	Type	Description	Default
`model_config`	`GaussianMixtureNoiseModel`	description	required

Returns:

Type	Description
`_description_`