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searchindex.js
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Search.setIndex({"alltitles": {"(Accelerated) Proximal Gradient Descent (PGD) \ud83d\udd17": [[53, "(Accelerated)-Proximal-Gradient-Descent-(PGD)-\ud83d\udd17"]], "0) Install dependencies": [[22, "0)-Install-dependencies"]], "1) Prepare data": [[22, "1)-Prepare-data"]], "2) Convolve image": [[22, "2)-Convolve-image"]], "2D Imaging": [[23, "2D-Imaging"]], "3) Benchmark convolution runtime across all libraries": [[22, "3)-Benchmark-convolution-runtime-across-all-libraries"]], "A Nod to Deep Learning \ud83d\ude80": [[57, "A-Nod-to-Deep-Learning-\ud83d\ude80"]], "A Non-Ideal Parallel-beam Tomographic Setup": [[66, "A-Non-Ideal-Parallel-beam-Tomographic-Setup"]], "API Reference": [[3, "api-reference"]], "API Rules": [[25, "api-rules"]], "Accessing Lipschitz Constants": [[60, "Accessing-Lipschitz-Constants"]], "Adding Noise to the Image": [[54, "Adding-Noise-to-the-Image"]], "Additional Features of LinOp: Batteries Included": [[57, "Additional-Features-of-LinOp:-Batteries-Included"]], "Advanced Computerized Tomography with Pyxu": [[23, "Advanced-Computerized-Tomography-with-Pyxu"]], "Advanced Usage: Guru Interface": [[53, "Advanced-Usage:-Guru-Interface"]], "Algorithms Overview": [[53, "Algorithms-Overview"]], "Applying the Blurring and Adding Noise": [[19, "Applying-the-Blurring-and-Adding-Noise"]], "Arithmetic Operations on Operators": [[52, "Arithmetic-Operations-on-Operators"]], "Arithmetic Rules (low-level)": [[3, "arithmetic-rules-low-level"]], "Array Backend-Related": [[3, "array-backend-related"]], "Automatic deployment and version management": [[24, "automatic-deployment-and-version-management"]], "Basic Equations": [[66, "Basic-Equations"]], "Basic Installation": [[64, "basic-installation"]], "Basic Operators": [[3, "basic-operators"], [12, "basic-operators"]], "Bayesian Computational Imaging": [[65, "Bayesian-Computational-Imaging"]], "Bayesian Computational Imaging with Pyxu": [[54, "Bayesian-Computational-Imaging-with-Pyxu"]], "Bayesian Inversion": [[66, "Bayesian-Inversion"]], "Behind the Scenes: Arithmetic Rules": [[52, "Behind-the-Scenes:-Arithmetic-Rules"]], "Block-defined Operators": [[3, "block-defined-operators"]], "Building Block-Operators": [[52, "Building-Block-Operators"]], "CSEEG": [[33, "cseeg"]], "Catalogue": [[28, "catalogue"]], "Catalogue Website": [[27, "catalogue-website"]], "Choosing the Right Algorithm": [[53, "Choosing-the-Right-Algorithm"]], "Combining the Likelihood and Prior": [[54, "Combining-the-Likelihood-and-Prior"]], "Comparative Analysis": [[62, "comparative-analysis"]], "Comparison with other Frameworks": [[62, "comparison-with-other-frameworks"]], "Complex Number Handling": [[3, "complex-number-handling"]], "Components contributed": [[29, "components-contributed"], [30, "components-contributed"], [31, "components-contributed"], [32, "components-contributed"], [33, "components-contributed"], [34, "components-contributed"], [35, "components-contributed"], [36, "components-contributed"], [37, "components-contributed"], [38, "components-contributed"], [39, "components-contributed"], [40, "components-contributed"], [41, "components-contributed"], [42, "components-contributed"], [43, "components-contributed"], [44, "components-contributed"], [45, "components-contributed"], [46, "components-contributed"], [47, "components-contributed"], [49, "components-contributed"], [50, "components-contributed"]], "Computation times": [[21, "computation-times"], [68, "computation-times"]], "Computational Imaging in a Nutshell": [[65, "Computational-Imaging-in-a-Nutshell"]], "Conclusion": [[18, "Conclusion"], [62, "conclusion"]], "Conjugate Gradient (CG) \ud83d\udd17": [[53, "Conjugate-Gradient-(CG)-\ud83d\udd17"]], "Continuous Integration": [[24, "continuous-integration"]], "Contributing to the Pyxu-FAIR": [[24, "contributing-to-the-pyxu-fair"]], "Contributors": [[61, "contributors"]], "Convolution with Pyxu": [[22, "Convolution-with-Pyxu"]], "Core Methods": [[57, "Core-Methods"]], "Crafting Custom Loss Functionals through Composition with Forward Operators": [[56, "Crafting-Custom-Loss-Functionals-through-Composition-with-Forward-Operators"]], "Create blurring kernel": [[22, "Create-blurring-kernel"]], "Create input image": [[22, "Create-input-image"]], "Create your documentation": [[24, "create-your-documentation"]], "Create your plugin package": [[24, "create-your-plugin-package"]], "Creating the Blurring Kernel": [[19, "Creating-the-Blurring-Kernel"]], "DSP-Notebooks": [[34, "dsp-notebooks"]], "DeepInv: A Note on Usability": [[62, "deepinv-a-note-on-usability"]], "Defining the Likelihood Function": [[54, "Defining-the-Likelihood-Function"]], "Defining the Prior Distribution": [[54, "Defining-the-Prior-Distribution"]], "Demystifying the Adjoint": [[57, "Demystifying-the-Adjoint"]], "Demystifying the Proximal Operator \ud83c\udfad": [[56, "Demystifying-the-Proximal-Operator-\ud83c\udfad"]], "Derivatives": [[3, "derivatives"], [12, "derivatives"]], "Description": [[33, "description"], [34, "description"], [35, "description"], [36, "description"], [37, "description"], [38, "description"], [39, "description"], [40, "description"], [41, "description"], [42, "description"], [43, "description"], [44, "description"], [45, "description"], [46, "description"], [47, "description"], [49, "description"], [50, "description"]], "Detailed information": [[29, "detailed-information"], [30, "detailed-information"], [31, "detailed-information"], [32, "detailed-information"], [33, "detailed-information"], [34, "detailed-information"], [35, "detailed-information"], [36, "detailed-information"], [37, "detailed-information"], [38, "detailed-information"], [39, "detailed-information"], [40, "detailed-information"], [41, "detailed-information"], [42, "detailed-information"], [43, "detailed-information"], [44, "detailed-information"], [45, "detailed-information"], [46, "detailed-information"], [47, "detailed-information"], [49, "detailed-information"], [50, "detailed-information"]], "Develop new features": [[24, "develop-new-features"]], "Developer Installation": [[64, "developer-installation"]], "Developer Notes": [[25, "developer-notes"]], "DiffFunc: Differentiable Functionals \ud83c\udfaf": [[56, "DiffFunc:-Differentiable-Functionals-\ud83c\udfaf"]], "DiffMap for Non-linear Forward Operators": [[57, "DiffMap-for-Non-linear-Forward-Operators"]], "Differential Operators in Pyxu": [[55, "Differential-Operators-in-Pyxu"]], "Direct 2d convolution": [[22, "Direct-2d-convolution"]], "Distributed and Out-of-core Computing with Dask": [[58, "Distributed-and-Out-of-core-Computing-with-Dask"]], "Divide and Conquer Strategy": [[57, "Divide-and-Conquer-Strategy"]], "Ease-of-Use": [[62, "ease-of-use"]], "Ecosystem": [[61, "ecosystem"]], "Element-wise Operators": [[3, "element-wise-operators"], [13, "element-wise-operators"]], "Embracing GPU Computing with CuPy": [[58, "Embracing-GPU-Computing-with-CuPy"]], "EnvironTracker": [[35, "environtracker"]], "Estimating Lipschitz Constants": [[60, "Estimating-Lipschitz-Constants"]], "Example Gallery": [[20, "example-gallery"]], "Example Usage": [[53, "Example-Usage"]], "Example of a rule-abiding operator": [[25, "example-of-a-rule-abiding-operator"]], "Extending Pyxu": [[27, "extending-pyxu"]], "Fan Beam": [[23, "Fan-Beam"]], "Feature Maturity - Comparison": [[62, "id2"]], "Features and Maturity": [[62, "features-and-maturity"]], "Filters": [[3, "filters"], [12, "filters"]], "Final Thoughts": [[58, "Final-Thoughts"]], "Finite Differences Approximation to the Partial Derivative": [[55, "Finite-Differences-Approximation-to-the-Partial-Derivative"]], "First, import the necessary modules:": [[54, "First,-import-the-necessary-modules:"]], "For Developers": [[26, "for-developers"]], "For Pyxu Users": [[26, "for-pyxu-users"]], "Forward Operators": [[57, "Forward-Operators"]], "Func: The Foundation Stone \ud83e\uddf1": [[56, "Func:-The-Foundation-Stone-\ud83e\uddf1"]], "Functionals": [[3, "functionals"]], "Functionals Hierarchy in Pyxu": [[56, "Functionals-Hierarchy-in-Pyxu"]], "Gaussian Derivative Approximation to the Partial Derivative": [[55, "Gaussian-Derivative-Approximation-to-the-Partial-Derivative"]], "General": [[3, "general"], [8, "general"]], "General information": [[29, "general-information"], [30, "general-information"], [31, "general-information"], [32, "general-information"], [33, "general-information"], [34, "general-information"], [35, "general-information"], [36, "general-information"], [37, "general-information"], [38, "general-information"], [39, "general-information"], [40, "general-information"], [41, "general-information"], [42, "general-information"], [43, "general-information"], [44, "general-information"], [45, "general-information"], [46, "general-information"], [47, "general-information"], [49, "general-information"], [50, "general-information"]], "Get Started Now!": [[63, "get-started-now"]], "Getting Started": [[63, "getting-started"]], "Governance and Team": [[61, "governance-and-team"]], "Gradient": [[55, "Gradient"]], "HPC Features - Comparison": [[62, "id3"]], "HVOX": [[36, "hvox"]], "Hands-On Example \ud83c\udf93": [[60, "Hands-On-Example-\ud83c\udf93"]], "Hands-on Example:": [[58, "Hands-on-Example:"]], "Hands-on Example: Computerized Tomography with Pyxu": [[66, "Hands-on-Example:-Computerized-Tomography-with-Pyxu"]], "Hessian": [[55, "Hessian"]], "High Performance Computing Features": [[58, "High-Performance-Computing-Features"]], "High-Performance Computing Features in Pyxu": [[58, "High-Performance-Computing-Features-in-Pyxu"]], "HoughDetector": [[37, "houghdetector"]], "How Does it Work? \ud83d\udee0\ufe0f": [[52, "How-Does-it-Work?-\ud83d\udee0\ufe0f"]], "How does this happens?": [[26, "how-does-this-happens"]], "How to choose between Finite Differences and Gaussian Derivative?": [[55, "How-to-choose-between-Finite-Differences-and-Gaussian-Derivative?"]], "How to use plugins in Pyxu?": [[26, "how-to-use-plugins-in-pyxu"]], "Hyperparameter Tuning": [[53, "Hyperparameter-Tuning"]], "Image Reconstruction with Pyxu": [[66, "Image-Reconstruction-with-Pyxu"]], "Implementing New Algorithms": [[53, "Implementing-New-Algorithms"]], "Implementing with Pyxu": [[54, "Implementing-with-Pyxu"]], "Implicit Functionals: The Undercover Agents \ud83d\udd75\ufe0f\u200d\u2640\ufe0f": [[56, "Implicit-Functionals:-The-Undercover-Agents-\ud83d\udd75\ufe0f\u200d\u2640\ufe0f"]], "Indicator Functions": [[3, "indicator-functions"], [10, "indicator-functions"]], "Initialize a git repository in your package": [[24, "initialize-a-git-repository-in-your-package"]], "Installation": [[64, "installation"]], "Installation with Optional Dependencies": [[64, "installation-with-optional-dependencies"]], "Interoperability Protocol": [[27, "interoperability-protocol"]], "Interoperation with Deep Learning Frameworks": [[64, "interoperation-with-deep-learning-frameworks"]], "Introduction to Lipschitz Constants": [[60, "Introduction-to-Lipschitz-Constants"]], "JAX": [[3, "jax"], [8, "jax"]], "Join Our Community": [[63, "join-our-community"]], "Key Features & Capabilities": [[61, "key-features-capabilities"]], "Linear Operators": [[3, "linear-operators"]], "Lipschitz Constants and Automatic Step Size Tuning": [[60, "Lipschitz-Constants-and-Automatic-Step-Size-Tuning"]], "Loading and Preprocessing the Image": [[19, "Loading-and-Preprocessing-the-Image"], [54, "Loading-and-Preprocessing-the-Image"]], "Loss & Regularization Functionals": [[56, "Loss-&-Regularization-Functionals"]], "MAP Approach with Total Variation Prior and Positivity Constraint": [[54, "MAP-Approach-with-Total-Variation-Prior-and-Positivity-Constraint"]], "MAP Estimate with Composite Positivity + Total Variation Prior": [[19, "MAP-Estimate-with-Composite-Positivity-+-Total-Variation-Prior"]], "Main Contenders": [[62, "main-contenders"]], "Meta-programming Framework": [[27, "meta-programming-framework"]], "Misc": [[3, "misc"], [3, "id3"], [13, "misc"]], "Module-Agnostic Infrastructure": [[58, "Module-Agnostic-Infrastructure"]], "Monitor testing and coverage": [[24, "monitor-testing-and-coverage"]], "Moreau Envelope for Smoothing": [[56, "Moreau-Envelope-for-Smoothing"]], "Naive Application of Filtered-Back Projection": [[66, "Naive-Application-of-Filtered-Back-Projection"]], "Norms & Loss Functions": [[3, "norms-loss-functions"], [10, "norms-loss-functions"]], "NumPy and Its Siblings: CuPy and Dask": [[58, "NumPy-and-Its-Siblings:-CuPy-and-Dask"]], "Obtaining and Visualizing the Denoised Image": [[54, "Obtaining-and-Visualizing-the-Denoised-Image"]], "Operator Algebra Logic": [[52, "Operator-Algebra-Logic"]], "Operator Algebra and Lipschitz Constant Propagation": [[60, "Operator-Algebra-and-Lipschitz-Constant-Propagation"]], "Operator-Related": [[3, "id2"]], "Operator-related": [[3, "operator-related"]], "Optimization Algorithms": [[53, "Optimization-Algorithms"]], "OrientationPy": [[38, "orientationpy"]], "PYFW": [[39, "pyfw"]], "Palentologist": [[40, "palentologist"]], "Parallel Beam: Uniform Offsets": [[23, "Parallel-Beam:-Uniform-Offsets"]], "Parameters": [[55, "Parameters"]], "Parameters (__init__())": [[14, "parameters-init"], [14, "id3"], [14, "id6"], [14, "id10"], [14, "id17"], [14, "id25"], [14, "id35"], [14, "id39"], [14, "id48"], [14, "id58"]], "Parameters (fit())": [[14, "parameters-fit"], [14, "id4"], [14, "id7"], [14, "id11"], [14, "id18"], [14, "id26"], [14, "id32"], [14, "id36"], [14, "id40"], [14, "id44"], [14, "id49"], [14, "id53"], [14, "id59"]], "Partial Derivative Parametrization": [[55, "Partial-Derivative-Parametrization"]], "Partial Derivatives": [[55, "Partial-Derivatives"]], "Partners & Sponsors": [[61, "partners-sponsors"]], "PhaseRet": [[41, "phaseret"]], "Plug-and-Play Reconstruction Schemes": [[66, "Plug-and-Play-Reconstruction-Schemes"]], "Plugin Preview Catalog": [[48, "plugin-preview-catalog"]], "PnP Priors: Implicit yet Intuitive": [[66, "PnP-Priors:-Implicit-yet-Intuitive"]], "Practical Example: Deblurring through Least-Squares \ud83c\udf20": [[56, "Practical-Example:-Deblurring-through-Least-Squares-\ud83c\udf20"]], "Pre-commit": [[24, "id1"]], "Precision Context Manager": [[58, "Precision-Context-Manager"]], "Preliminaries": [[23, "Preliminaries"]], "Primal-Dual Splitting (PDS) Methods": [[53, "Primal-Dual-Splitting-(PDS)-Methods"]], "ProxFunc: Proximable Functionals \ud83d\udee1\ufe0f": [[56, "ProxFunc:-Proximable-Functionals-\ud83d\udee1\ufe0f"]], "Pseudoinverse Solution": [[66, "Pseudoinverse-Solution"]], "PyLops": [[22, "PyLops"]], "PyTorch": [[3, "pytorch"], [8, "pytorch"]], "PycGSP": [[42, "pycgsp"]], "PycSphere": [[43, "pycsphere"]], "Pyxu": [[22, "Pyxu"], [61, "pyxu"]], "Pyxu Score Explained": [[51, "pyxu-score-explained"]], "Pyxu: High-Performance Computational Imaging with Python": [[65, "Pyxu:-High-Performance-Computational-Imaging-with-Python"]], "Pyxu\u2019s Modern Take on HPC": [[58, "Pyxu's-Modern-Take-on-HPC"]], "Pyxu\u2019s Modularity to the Rescue": [[66, "Pyxu's-Modularity-to-the-Rescue"]], "Quality Assurance for Adjoint Operators in Pyxu": [[57, "Quality-Assurance-for-Adjoint-Operators-in-Pyxu"]], "References": [[67, "references"]], "Remark": [[12, "remark"], [12, null]], "Remarks": [[2, "remarks"], [14, "remarks"], [14, "id9"], [14, "id14"], [14, "id21"], [14, "id28"], [14, "id33"], [14, "id37"], [14, "id41"], [14, "id45"], [14, "id50"], [14, "id54"]], "Running tests locally": [[24, "running-tests-locally"]], "SCICO: A Closer Look": [[62, "scico-a-closer-look"]], "Sampling Tools": [[3, "sampling-tools"]], "SciPy": [[3, "scipy"], [8, "scipy"]], "Scico": [[22, "Scico"]], "Scipy": [[22, "Scipy"]], "Separable 1d convolution": [[22, "Separable-1d-convolution"]], "Set up automatic deployments": [[24, "set-up-automatic-deployments"]], "Setup a local environment": [[24, "setup-a-local-environment"]], "Simplifying the Optimization Problem": [[54, "Simplifying-the-Optimization-Problem"]], "Solver-related": [[3, "solver-related"]], "Specialized Classes: ProxDiffFunc, LinFunc, QuadraticFunc \ud83c\udfa8": [[56, "Specialized-Classes:-ProxDiffFunc,-LinFunc,-QuadraticFunc-\ud83c\udfa8"]], "Stacks of Partial Derivatives": [[55, "Stacks-of-Partial-Derivatives"]], "Steering Council": [[61, "steering-council"]], "Stencils & Convolutions": [[3, "stencils-convolutions"], [12, "stencils-convolutions"]], "Step 1: Attempting to Import Before Installation": [[18, "Step-1:-Attempting-to-Import-Before-Installation"]], "Step 2: Installing the Plugin": [[18, "Step-2:-Installing-the-Plugin"]], "Step 3: Importing the Necessary Objects": [[18, "Step-3:-Importing-the-Necessary-Objects"]], "Step 4: Using the Gradient Descent Algorithm": [[18, "Step-4:-Using-the-Gradient-Descent-Algorithm"]], "Support for HPC Computing": [[62, "support-for-hpc-computing"]], "Supported Backends \ud83c\udf9b\ufe0f": [[60, "Supported-Backends-\ud83c\udf9b\ufe0f"]], "TVDenoiser": [[44, "tvdenoiser"]], "Table 1: Choice of cost functional based on noise modeling": [[54, "Table-1:-Choice-of-cost-functional-based-on-noise-modeling"]], "Table 2: Choice of regularization functional based on the prior distribution": [[54, "Table-2:-Choice-of-regularization-functional-based-on-the-prior-distribution"]], "Table of Contents": [[0, "table-of-contents"], [3, "table-of-contents"], [8, "table-of-contents"], [10, "table-of-contents"], [12, "table-of-contents"], [13, "table-of-contents"], [17, "table-of-contents"]], "Tensor Products": [[3, "tensor-products"], [12, "tensor-products"]], "The Adoptability and Usability Crisis of Computational Imaging": [[65, "The-Adoptability-and-Usability-Crisis-of-Computational-Imaging"]], "The Benefit: Automatic Propagation \ud83d\ude80": [[56, "The-Benefit:-Automatic-Propagation-\ud83d\ude80"]], "The Conundrum of Performance vs Modularity": [[58, "The-Conundrum-of-Performance-vs-Modularity"]], "The Dawn of Computational Imaging": [[65, "The-Dawn-of-Computational-Imaging"]], "The Deep Learning Revolution": [[65, "The-Deep-Learning-Revolution"]], "The Importance of Matrix-Free Operators": [[57, "The-Importance-of-Matrix-Free-Operators"]], "The Multi-faceted Realm of Computational Imaging": [[65, "The-Multi-faceted-Realm-of-Computational-Imaging"]], "The Takeaway: Flexibility and Power \ud83c\udf08": [[56, "The-Takeaway:-Flexibility-and-Power-\ud83c\udf08"]], "TokamakRec": [[45, "tokamakrec"]], "Tomographic Reconstruction in a Nutshell": [[66, "Tomographic-Reconstruction-in-a-Nutshell"]], "Total-Variation based Bayesian Image Deblurring": [[19, "Total-Variation-based-Bayesian-Image-Deblurring"]], "Transforms": [[3, "transforms"], [12, "transforms"]], "UncertaintyQuant": [[46, "uncertaintyquant"]], "Understanding the Problem": [[54, "Understanding-the-Problem"]], "Upload it to GitHub": [[24, "upload-it-to-github"]], "User Guide": [[59, "user-guide"]], "Using Contributed Plugins in Pyxu": [[18, 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