Reconstruction¶

Check out this notebook on Google Colab for an overview of the reconstruction algorithms available in LenslessPiCam (analytic and learned).

The core algorithmic component of LenslessPiCam is the abstract class ReconstructionAlgorithm. The five reconstruction strategies available in LenslessPiCam derive from this class:

GradientDescent: projected gradient descent with a non-negativity constraint. Two accelerated approaches are also available: NesterovGradientDescent and FISTA.
ADMM: alternating direction method of multipliers (ADMM) with a non-negativity constraint and a total variation (TV) regularizer 1.
APGD: accelerated proximal gradient descent with Pycsou as a backend. Any differentiable or proximal operator can be used as long as it is compatible with Pycsou, namely derives from one of DiffFunc or ProxFunc.
UnrolledFISTA: unrolled FISTA with a non-negativity constraint.
UnrolledADMM: unrolled ADMM with a non-negativity constraint and a total variation (TV) regularizer 1.

Note that the unrolled algorithms derive from the abstract class TrainableReconstructionAlgorithm, which itself derives from ReconstructionAlgorithm while adding functionality for training on batches and adding trainable pre- and post-processing blocks.

New reconstruction algorithms can be conveniently implemented by deriving from the abstract class and defining the following abstract methods:

the update step: _update.
a method to reset state variables: reset.
an image formation method: _form_image.

One advantage of deriving from ReconstructionAlgorithm is that functionality for iterating, saving, and visualization is already implemented. Consequently, using a reconstruction algorithm that derives from it boils down to three steps:

Creating an instance of the reconstruction algorithm.
Setting the data.
Applying the algorithm.

2D example (ADMM)¶

For example, for ADMM:

recon = ADMM(psf)
recon.set_data(data)
res = recon.apply(n_iter=n_iter)

A full running example can found in scripts/recon/admm.py and run as:

python scripts/recon/admm.py

Note that a YAML configuration script is defined in configs/admm_thumbs_up.yaml, which is used by default. Individual parameters can be configured as such:

python scripts/recon/admm.py admm.n_iter=10 preprocess.gray=True

--help can be used to view all available parameters.

>> python scripts/recon/admm.py --help

...

== Config ==
Override anything in the config (foo.bar=value)

files:
    psf: data/psf/tape_rgb.png
    data: data/raw_data/thumbs_up_rgb.png
preprocess:
    downsample: 4
    shape: null
    flip: false
    bayer: false
    blue_gain: null
    red_gain: null
    single_psf: false
    gray: false
display:
    disp: 1
    plot: true
    gamma: null
save: false
admm:
    n_iter: 5
    mu1: 1.0e-06
    mu2: 1.0e-05
    mu3: 4.0e-05
    tau: 0.0001

...

Alternatively, a new configuration file can be defined in the configs folder and passed to the script:

python scripts/recon/admm.py -cn <CONFIG_FILENAME_WITHOUT_YAML_EXT>

3D example¶

It is also possible to reconstruct 3D scenes using GradientDescent or APGD. ADMM does not support 3D reconstruction yet. This requires to use a 3D PSF as an input in the form of an .npy or .npz file, which is a set of 2D PSFs corresponding to the same diffuser sampled with light sources at different depths. The input data for 3D reconstructions is still a 2D image, as collected by the camera. The reconstruction will be able to separate which part of the lensless data corresponds to which 2D PSF, and therefore to which depth, effectively generating a 3D reconstruction, which will be outputed in the form of an .npy file. A 2D projection on the depth axis is also displayed to the user.

The same scripts for 2D reconstruction can be used for 3D reconstruction, namely scripts/recon/gradient_descent.py and scripts/recon/apgd_pycsou.py.

3D data is provided in LenslessPiCam, but it is simulated. Real example data can be obtained from Waller Lab. For both the simulated data and the data from Waller Lab, it is best to set downsample=1:

python scripts/recon/gradient_descent.py \
input.psf="path/to/3D/psf.npy" \
input.data="path/to/lensless/data.tiff" \
preprocess.downsample=1

Other approaches¶

Scripts for other reconstruction algorithms can be found in scripts/recon and their corresponding configurations in configs.

References

1(1,2): Boyd, S., Parikh, N., & Chu, E. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Now Publishers Inc.

Reconstruction API¶

Abstract Class¶

class lensless.ReconstructionAlgorithm(psf, dtype=None, pad=True, n_iter=100, initial_est=None, reset=True, denoiser=None, **kwargs)[source]¶

Abstract class for defining lensless imaging reconstruction algorithms.

The following abstract methods need to be defined:

_update: updating state variables at each iterations.
reset: reset state variables.
_form_image: any pre-processing that needs to be done in order to view the image estimate, e.g. reshaping or clipping.

One advantage of deriving from this abstract class is that functionality for iterating, saving, and visualization is already implemented, namely in the apply method.

Consequently, using a reconstruction algorithm that derives from it boils down to three steps:

Creating an instance of the reconstruction algorithm.
Setting the data.
Applying the algorithm.

__init__(psf, dtype=None, pad=True, n_iter=100, initial_est=None, reset=True, denoiser=None, **kwargs)[source]¶

Base constructor. Derived constructor may define new state variables here and also reset them in reset.

Parameters

psf (ndarray or Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization.
pad (bool, optional) – Whether data needs to be padded prior to convolution. User may wish to optimize padded data and set this to False, as is done for ADMM. Defaults to True.
n_iter (int, optional) – Number of iterations to run algorithm for. Can be overridden in apply.
initial_est (ndarray or Tensor, optional) – Initial estimate of the image. If not provided, the initial estimate is set to zero or to the mean of the data, depending on the algorithm.
reset (bool, optional) – Whether to reset state variables in the base constructor. Defaults to True. If False, you should call reset() at one point to initialize state variables.
denoiser (dict, optional) –
Dictionary defining a denoiser for plug-and-play. Must contain the following keys:
- "network": model to use as a denoiser.
- "noise_level": noise level of the denoiser.
If provided, the denoiser will be used as a projection function at each iteration. Defaults to None.

abstract _form_image()[source]¶: Any pre-processing to form a viewable image, e.g. reshaping or clipping.

abstract _update(iter)[source]¶: Update state variables.

apply(n_iter=None, disp_iter=- 1, plot_pause=0.2, plot=False, save=False, gamma=None, ax=None, reset=True, background=None, **kwargs)[source]¶

Method for performing iterative reconstruction. Note that set_data must be called beforehand.

Parameters

n_iter (int, optional) – Number of iterations. If not provided, default to self._n_iter.
disp_iter (int) – How often to display and/or intermediate reconstruction (in number of iterations). If None OR plot or save are False, no intermediate reconstruction will be plotted/saved.
plot_pause (float) – Number of seconds to pause after displaying reconstruction.
plot (bool) – Whether to plot final result, and intermediate results if disp_iter is not None.
save (bool) – Whether to save final result (as PNG), and intermediate results if disp_iter is not None.
gamma (float, optional) – Gamma correction factor to apply for plots. Default is None.
ax (Axes, optional) – Axes object to fill for plotting/saving, default is to create one.
reset (bool, optional) – Whether to reset state variables before applying reconstruction. Default to True. Set to false if continuing reconstruction from previous state.

Returns

final_im (ndarray) – Final reconstruction.
ax (Axes) – Axes object on which final reconstruction is displayed. Only returning if plot or save is True.

get_image_estimate()[source]¶: Get current image estimate as [Batch, Depth, Height, Width, Channels].

reconstruction_error(prediction=None, lensless=None, psfs=None, normalize=True)[source]¶

Compute reconstruction error.

Parameters

prediction (ndarray or Tensor, optional) – Reconstructed image. If None, use current estimate, default None.
lensless (ndarray or Tensor, optional) – Lensless image. If None, use data provided by set_data(), default None.

Returns

_description_

Return type

_type_

abstract reset()[source]¶: Reset state variables.

set_data(data)[source]¶

Set lensless data for recontruction.

Parameters: data (ndarray) – Lensless data on which to iterate to recover an estimate of the scene. Should match provide PSF, i.e. shape and 2D (grayscale) or 3D (RGB).

set_image_estimate(image_est)[source]¶

Set initial estimate of image, e.g. to warm-start algorithm.

Parameters: image_est (ndarray or Tensor) – Initial estimate of the image. Should match provide PSF shape.

Gradient Descent¶

class lensless.GradientDescent(psf, dtype=None, proj=<function non_neg>, lip_fact=1.8, **kwargs)[source]¶

Object for applying projected gradient descent.

__init__(psf, dtype=None, proj=<function non_neg>, lip_fact=1.8, **kwargs)[source]¶

Parameters

psf (ndarray or Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization. Default is float32.
proj (function) – Projection function to apply at each iteration. Default is non-negative.

class lensless.NesterovGradientDescent(psf, dtype=None, proj=<function non_neg>, p=0, mu=0.9, **kwargs)[source]¶

Object for applying projected gradient descent with Nesterov momentum for acceleration.

A nice tutorial/ blog post on Nesterov momentum can be found here.

__init__(psf, dtype=None, proj=<function non_neg>, p=0, mu=0.9, **kwargs)[source]¶

Parameters

psf (ndarray or Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization. Default is float32.
proj (function) – Projection function to apply at each iteration. Default is non-negative.
p (float) – Momentum parameter that keeps track of changes. By default, this is initialized to 0.
mu (float) – Momentum parameter. Default is 0.9.

class lensless.FISTA(psf, dtype=None, proj=<function non_neg>, tk=1.0, **kwargs)[source]¶

Object for applying projected gradient descent with FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) for acceleration.

Paper: https://www.ceremade.dauphine.fr/~carlier/FISTA

__init__(psf, dtype=None, proj=<function non_neg>, tk=1.0, **kwargs)[source]¶

Parameters

psf (ndarray or Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization. Default is float32.
proj (function) – Projection function to apply at each iteration. Default is non-negative.
tk (float) – Initial step size parameter for FISTA. It is updated at each iteration according to Eq. 4.2 of paper. By default, initialized to 1.0.

lensless.recon.gd.non_neg(xi)[source]¶

Clip input so that it is non-negative.

Parameters: xi (ndarray) – Data to clip.
Returns: nonneg – Non-negative projection of input.
Return type: ndarray

ADMM¶

class lensless.ADMM(psf, dtype=None, mu1=1e-06, mu2=1e-05, mu3=4e-05, tau=0.0001, psi=None, psi_adj=None, psi_gram=None, pad=False, norm='backward', denoiser=None, **kwargs)[source]¶

Object for applying ADMM (Alternating Direction Method of Multipliers) with a non-negativity constraint and a total variation (TV) prior.

Paper about ADMM: https://web.stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf

Slides about ADMM: https://web.stanford.edu/class/ee364b/lectures/admm_slides.pdf

__init__(psf, dtype=None, mu1=1e-06, mu2=1e-05, mu3=4e-05, tau=0.0001, psi=None, psi_adj=None, psi_gram=None, pad=False, norm='backward', denoiser=None, **kwargs)[source]¶

Parameters

psf (ndarray or Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization. Default is float32.
mu1 (float) – Step size for updating primal/dual variables.
mu2 (float) – Step size for updating primal/dual variables.
mu3 (float) – Step size for updating primal/dual variables.
tau (float) – Weight for L1 norm of psi applied to the image estimate.
psi (function, optional) – Operator to map image to a space that the image is assumed to be sparse in (hence L1 norm). Default is to use total variation (TV) operator.
psi_adj (function) – Adjoint of psi.
psi_gram (function) – Function to compute gram of psi.
pad (bool) – Whether to pad the image with zeros before applying the PSF. Default is False, as optimized data is already padded.
norm (str) – Normalization to use for the convolution. Options are “forward”, “backward”, and “ortho”. Default is “backward”.

lensless.recon.admm.soft_thresh(x, thresh)[source]¶

lensless.recon.admm.finite_diff(x)[source]¶: Gradient of image estimate, approximated by finite difference. Space where image is assumed sparse.

lensless.recon.admm.finite_diff_adj(x)[source]¶: Adjoint of finite difference operator.

lensless.recon.admm.finite_diff_gram(shape, dtype=None, is_torch=False)[source]¶: Gram matrix of finite difference operator.

Tikhonov (Ridge Regression)¶

class lensless.CodedApertureReconstruction(mask, image_shape, P=None, Q=None, lmbd=0.0003)[source]¶

Reconstruction method for the (non-iterative) Tikhonov algorithm presented in the FlatCam paper.

TODO: operations in float32

__init__(mask, image_shape, P=None, Q=None, lmbd=0.0003)[source]¶

Parameters

mask (py:class:lensless.hardware.mask.CodedAperture) – Coded aperture mask object.
image_shape ((array-like or tuple)) – The shape of the image to reconstruct.
P (ndarray, optional) – Left convolution matrix in measurement operator. Must be of shape (measurement_resolution[0], image_shape[0]). By default, it is generated from the mask. In practice, it may be useful to measure as in the FlatCam paper.
Q (ndarray, optional) – Right convolution matrix in measurement operator. Must be of shape (measurement_resolution[1], image_shape[1]). By default, it is generated from the mask. In practice, it may be useful to measure as in the FlatCam paper.
lmbd (float:) – Regularization parameter. Default value is 3e-4 as in the FlatCam paper code.

apply(img)[source]¶

Method for performing Tikhinov reconstruction.

Parameters: img (ndarray or torch.Tensor) – Lensless capture measurement. Must be 3D even if grayscale.
Returns: Reconstructed image, in the same format as the measurement.
Return type: ndarray or Tensor

Accelerated Proximal Gradient Descent (APGD)¶

class lensless.recon.apgd.APGD(psf, max_iter=500, dtype='float32', diff_penalty=None, prox_penalty='nonneg', acceleration=True, diff_lambda=0.001, prox_lambda=0.001, disp=100, rel_error=None, lipschitz_tight=True, lipschitz_tol=1.0, img_shape=None, **kwargs)[source]¶

__init__(psf, max_iter=500, dtype='float32', diff_penalty=None, prox_penalty='nonneg', acceleration=True, diff_lambda=0.001, prox_lambda=0.001, disp=100, rel_error=None, lipschitz_tight=True, lipschitz_tol=1.0, img_shape=None, **kwargs)[source]¶

Wrapper for Pycsou’s PGD (accelerated proximal gradient descent) applied to lensless imaging.

Parameters

psf (ndarray) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
max_iter (int, optional) – Maximal number of iterations.
dtype (float32 or float64) – Data type to use for optimization.
diff_penalty (None or str or DiffFunc) –
Differentiable functional to serve as prior / regularization term. Default is None. See DiffFunc.
prox_penalty (None or str or ProxFunc) –
Proximal functional to serve as prior / regularization term. Default is non-negative prior. See ProxFunc.
acceleration (bool, optional) – Whether to use acceleration or not. Default is True.
diff_lambda (float) – Weight of differentiable penalty.
prox_lambda (float) – Weight of proximal penalty.
disp (int, optional) – Display frequency. Default is 100.
rel_error (float, optional) – Relative error to stop optimization. Default is 1e-6.
lipschitz_tight (bool, optional) – Whether to use tight Lipschitz constant or not. Default is True.
lipschitz_tol (float, optional) – Tolerance to compute Lipschitz constant. Default is 1.
img_shape (tuple, optional) – Shape of measurement (H, W, C). If None, assume shape of PSF.

Trainable reconstruction API¶

Abstract Class (Trainable)¶

class lensless.TrainableReconstructionAlgorithm(psf, dtype=None, n_iter=1, pre_process=None, post_process=None, skip_unrolled=False, skip_pre=False, skip_post=False, return_intermediate=False, legacy_denoiser=False, compensation=None, compensation_residual=True, psf_network=None, psf_residual=True, direct_background_subtraction=False, background_network=None, integrated_background_subtraction=False, **kwargs)[source]¶

Bases: ReconstructionAlgorithm, Module

Abstract class for defining lensless imaging reconstruction algorithms with trainable parameters.

The following abstract methods need to be defined:

_update: updating state variables at each iterations.
reset: reset state variables.
_form_image: any pre-processing that needs to be done in order to view the image estimate, e.g. reshaping or clipping.

One advantage of deriving from this abstract class is that functionality for iterating, saving, and visualization is already implemented, namely in the apply method.

Consequently, using a reconstruction algorithm that derives from it boils down to four steps:

Creating an instance of the reconstruction algorithm.
Training the algorithm
Setting the data.
Applying the algorithm.

__init__(psf, dtype=None, n_iter=1, pre_process=None, post_process=None, skip_unrolled=False, skip_pre=False, skip_post=False, return_intermediate=False, legacy_denoiser=False, compensation=None, compensation_residual=True, psf_network=None, psf_residual=True, direct_background_subtraction=False, background_network=None, integrated_background_subtraction=False, **kwargs)[source]¶

Base constructor. Derived constructor may define new state variables here and also reset them in reset.

Parameters

psf (Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization.
n_iter (int) – Number of iterations for unrolled algorithm.
pre_process (function or Module, optional) – If function : Function to apply to the image estimate before algorithm. Its input most be (image to process, noise_level), where noise_level is a learnable parameter. If it include aditional learnable parameters, they will not be added to the parameter list of the algorithm. To allow for traning, the function must be autograd compatible. If Module : A DruNet compatible network to apply to the image estimate before algorithm. See utils.image.apply_denoiser for more details. The network will be included as a submodule of the algorithm and its parameters will be added to the parameter list of the algorithm. If this isn’t intended behavior, set requires_grad=False.
post_process (function or Module, optional) – If function : Function to apply to the image estimate after the whole algorithm. Its input most be (image to process, noise_level), where noise_level is a learnable parameter. If it include aditional learnable parameters, they will not be added to the parameter list of the algorithm. To allow for traning, the function must be autograd compatible. If Module : A DruNet compatible network to apply to the image estimate after the whole algorithm. See utils.image.apply_denoiser for more details. The network will be included as a submodule of the algorithm and its parameters will be added to the parameter list of the algorithm. If this isn’t intended behavior, set requires_grad=False.
skip_unrolled (bool, optional) – Whether to skip the unrolled algorithm and only apply the pre- or post-processor block (e.g. to just use a U-Net for reconstruction).
return_unrolled_output (bool, optional) – Whether to return the output of the unrolled algorithm if also using a post-processor block.
compensation (list, optional) – Number of channels for each intermediate output in compensation layer, as in “Robust Reconstruction With Deep Learning to Handle Model Mismatch in Lensless Imaging” (2021). Post-processor must be defined if compensation provided.
compensation_residual (bool, optional) – Whether to use residual connection in compensation layer.
psf_network (function or Module, optional) – Function or model to apply to PSF prior to camera inversion.
psf_residual (bool, optional) – Whether to use residual connection in PSF network.

apply(disp_iter=10, plot_pause=0.2, plot=True, save=False, gamma=None, ax=None, reset=True, output_intermediate=False, background=None)[source]¶

Method for performing iterative reconstruction. Contrary to non-trainable reconstruction algorithm, the number of iteration isn’t required. Note that set_data must be called beforehand.

Parameters

disp_iter (int) – How often to display and/or intermediate reconstruction (in number of iterations). If None OR plot or save are False, no intermediate reconstruction will be plotted/saved.
plot_pause (float) – Number of seconds to pause after displaying reconstruction.
plot (bool) – Whether to plot final result, and intermediate results if disp_iter is not None.
save (bool) – Whether to save final result (as PNG), and intermediate results if disp_iter is not None.
gamma (float, optional) – Gamma correction factor to apply for plots. Default is None.
ax (Axes, optional) – Axes object to fill for plotting/saving, default is to create one.
output_intermediate (bool, optional) – Whether to output intermediate reconstructions after preprocessing and before postprocessing.

Returns

final_im (Tensor) – Final reconstruction.
ax (Axes) – Axes object on which final reconstruction is displayed. Only returning if plot or save is True.

forward(batch, psfs=None, background=None)[source]¶

Method for performing iterative reconstruction on a batch of images. This implementation is a properly vectorized implementation of FISTA.

Parameters

batch (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.
psfs (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.

Returns

The reconstructed images.

Return type

Tensor of shape (batch, depth, channels, height, width)

abstract reset()¶: Reset state variables.

set_data(data)¶

Set lensless data for recontruction.

Parameters: data (ndarray) – Lensless data on which to iterate to recover an estimate of the scene. Should match provide PSF, i.e. shape and 2D (grayscale) or 3D (RGB).

Unrolled FISTA¶

class lensless.UnrolledFISTA(psf, n_iter=5, dtype=None, proj=<function non_neg>, learn_tk=True, tk=1, **kwargs)[source]¶

Bases: TrainableReconstructionAlgorithm

Object for applying unrolled projected gradient descent with FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) for acceleration.

FISTA Paper: https://www.ceremade.dauphine.fr/~carlier/FISTA

__init__(psf, n_iter=5, dtype=None, proj=<function non_neg>, learn_tk=True, tk=1, **kwargs)[source]¶

COnstructor for unrolled FISTA algorithm.

Parameters

psf (Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
n_iter (int, optional) – Number of iterations to unrolled, by default 5
dtype (float32 or float64) – Data type to use for optimization.
proj (function, optional) – Projection function to apply at each iteration, by default non_neg
learn_tk (bool, optional) – whether the tk parameters of FISTA should be learnt, by default True
tk (int, optional) – Initial value of tk, by default 1

forward(batch, psfs=None, background=None)¶

Method for performing iterative reconstruction on a batch of images. This implementation is a properly vectorized implementation of FISTA.

Parameters

batch (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.
psfs (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.

Returns

The reconstructed images.

Return type

Tensor of shape (batch, depth, channels, height, width)

Unrolled ADMM¶

class lensless.UnrolledADMM(psf, dtype=None, n_iter=5, mu1=1e-06, mu2=1e-05, mu3=4e-05, tau=0.0001, psi=None, psi_adj=None, psi_gram=None, pad=False, norm='backward', **kwargs)[source]¶

Bases: TrainableReconstructionAlgorithm

Object for applying unrolled version of ADMM.

__init__(psf, dtype=None, n_iter=5, mu1=1e-06, mu2=1e-05, mu3=4e-05, tau=0.0001, psi=None, psi_adj=None, psi_gram=None, pad=False, norm='backward', **kwargs)[source]¶

Parameters

psf (Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization. Default is float32.
n_iter (int, optional) – Number of iterations to unrolled, by default 5
mu1 (float) – Initial step size for updating primal/dual variables.
mu2 (float) – Initial step size for updating primal/dual variables.
mu3 (float) – Initial step size for updating primal/dual variables.
tau (float) – Initial weight for L1 norm of psi applied to the image estimate.
psi (function, optional) – Operator to map image to a space that the image is assumed to be sparse in (hence L1 norm). Default is to use total variation (TV) operator.
psi_adj (function) – Adjoint of psi.
psi_gram (function) – Function to compute gram of psi.
pad (bool, optional) – Whether to pad the image with zeros before applying the PSF.
norm (str) – Normalization to use for the convolution. Options are “forward”, “backward”, and “ortho”. Default is “backward”.

forward(batch, psfs=None, background=None)¶

Method for performing iterative reconstruction on a batch of images. This implementation is a properly vectorized implementation of FISTA.

Parameters

batch (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.
psfs (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.

Returns

The reconstructed images.

Return type

Tensor of shape (batch, depth, channels, height, width)

Trainable Inversion¶

class lensless.TrainableInversion(psf, dtype=None, K=0.0001, **kwargs)[source]¶

Bases: TrainableReconstructionAlgorithm

__init__(psf, dtype=None, K=0.0001, **kwargs)[source]¶

Constructor for trainable inversion component as proposed in the FlatNet work: https://siddiquesalman.github.io/flatnet/

Their implementation: https://github.com/siddiquesalman/flatnet/blob/d1dc179666a08df58c4bdf83c4274310ba3cd186/models/fftlayer.py#L70

Parameters

psf (Tensor) – Point spread function (PSF) that models forward propagation. Must be of shape (depth, height, width, channels) even if depth = 1 and channels = 1. You can use load_psf() to load a PSF from a file such that it is in the correct format.
dtype (float32 or float64) – Data type to use for optimization.
K (float) – Regularization parameter.

forward(batch, psfs=None, background=None)¶

Method for performing iterative reconstruction on a batch of images. This implementation is a properly vectorized implementation of FISTA.

Parameters

batch (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.
psfs (Tensor of shape (batch, depth, channels, height, width)) – The lensless images to reconstruct.

Returns

The reconstructed images.

Return type

Tensor of shape (batch, depth, channels, height, width)

Reconstruction¶

2D example (ADMM)¶

3D example¶

Other approaches¶

Reconstruction API¶

Abstract Class¶

Gradient Descent¶

ADMM¶

Tikhonov (Ridge Regression)¶

Accelerated Proximal Gradient Descent (APGD)¶

Trainable reconstruction API¶

Abstract Class (Trainable)¶

Unrolled FISTA¶

Unrolled ADMM¶

Trainable Inversion¶

Multi-Wiener Deconvolution Network¶

Reconstruction Utilities¶