Struct Admm 

pub struct Admm {
    pub iterations: usize,
    pub object_step: f64,
    pub penalty: f64,
    pub dual_relaxation: f64,
    pub batch_size: usize,
    pub epsilon: f64,
}

Linearized ADMM reconstruction for Fourier ptychographic microscopy.

Method

The algorithm splits each predicted detector field from the shared object by introducing an auxiliary field and a scaled dual variable. Each step alternates among a measurement-amplitude proximal update of the auxiliary fields, a pupil-preconditioned linearized update of the common object spectrum, and a scaled-dual update that drives the auxiliary and predicted fields toward consensus. This separates the nonlinear measurement constraint from the overlapping Fourier-patch consistency constraint.

For incoherently multiplexed data, the amplitude proximal is joint across all source modes in a frame. Auxiliary and scaled-dual fields are stored per frame-source mode in ReconstructionState for exact checkpoint resumption. The fixed-pupil linearization and multiplexed proximal used here are crate adaptations of the reference ADMM-FPM formulation.

Each iteration reports detector-field RMS residuals. The primal residual is r_k = A x_k - z_k, evaluated after the linearized object update, and the dual residual is s_k = rho (z_k - z_{k-1}). Here A x denotes the concatenated per-mode detector fields, including each mode of a multiplexed frame. Masked pixels and zero-weight frames are excluded. These residuals diagnose consensus and auxiliary-field motion; the solver does not use them as stopping criteria.

Reference

A. Wang, Z. Zhang, S. Wang, A. Pan, C. Ma, and B. Yao, “Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers” (2022), Cells 11(9), 1512.

Fields

iterations: usize

Number of complete passes through the acquisition schedule.

object_step: f64

Step size of the linearized, pupil-preconditioned object update.

penalty: f64

Positive augmented-Lagrangian penalty tying auxiliary fields to the fields predicted by the shared object.

dual_relaxation: f64

Scaled-dual update relaxation in the inclusive range 0..=2.

batch_size: usize

Number of measured frames supplied to each reconstruction step; the default processes every frame together.

epsilon: f64

Positive numerical floor used in normalizations and dark-field handling.

Implementations

impl Admm

pub fn iterations(self, iterations: usize) -> Self

Sets the number of complete acquisition-schedule passes; validation requires non-zero.

pub fn object_step(self, step: f64) -> Self

Sets the finite positive step size for the linearized object update.

pub fn penalty(self, penalty: f64) -> Self

Sets the finite positive augmented-Lagrangian consensus penalty.

pub fn dual_relaxation(self, relaxation: f64) -> Self

Sets finite scaled-dual relaxation in the inclusive interval [0, 2].

pub fn batch_size(self, batch_size: usize) -> Self

Sets the positive acquisition-frame batch size.

Trait Implementations

impl Clone for Admm

fn clone(&self) -> Admm

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Admm

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Admm

fn default() -> Self

Returns the “default value” for a type.

impl ReconstructionAlgorithm for Admm

type IterationMetrics = AdmmIterationMetrics

Algorithm-specific metrics emitted by each step and appended to the trace.

fn validate(&self) -> Result<()>

Validates solver parameters independently of a reconstruction problem.

fn step<M: MeasurementRead>( &mut self, problem: &ReconstructionProblem<M>, state: &mut ReconstructionState, batch: &Batch, _iteration: usize, ) -> Result<StepOutput<Self::IterationMetrics>>

Updates state for one scheduled batch in zero-based iteration.

fn iterations(&self) -> usize

Returns the requested number of complete schedule passes.

fn batch_size(&self) -> usize

Returns the number of measured frames combined into one step.

fn validate_problem<M: MeasurementRead>( &self, _problem: &ReconstructionProblem<M>, ) -> Result<()>

Validates solver requirements that depend on problem.

fn initialize<M: MeasurementRead>( &self, problem: &ReconstructionProblem<M>, ) -> Result<ReconstructionState>

Creates the default CPU-backed state for problem.

fn initialize_with_backend<M: MeasurementRead>( &self, problem: &ReconstructionProblem<M>, backend: Arc<dyn Backend>, ) -> Result<ReconstructionState>

Creates reconstruction state using the supplied execution backend.

fn canonicalize_state<M: MeasurementRead>( &self, _problem: &ReconstructionProblem<M>, _state: &mut ReconstructionState, ) -> Result<()>

Projects algorithm-owned ambiguities into a stable reported convention.

fn supports_joint_reconstruction(&self) -> bool

Reports whether the algorithm may run inside physical joint calibration.

fn run<M: MeasurementRead>( self, problem: &ReconstructionProblem<M>, ) -> Result<ReconstructionResult>

where Self: Sized,

Runs the algorithm with default sequential scheduling and no callbacks.

fn run_with_callbacks<M: MeasurementRead>( self, problem: &ReconstructionProblem<M>, callbacks: Vec<Box<dyn Callback>>, ) -> Result<ReconstructionResult>

where Self: Sized,

Runs the algorithm and invokes callbacks at their declared hooks.

fn run_from_checkpoint<M: MeasurementRead>( self, problem: &ReconstructionProblem<M>, checkpoint: ReconstructionCheckpoint, ) -> Result<ReconstructionResult>

where Self: Sized,

Resumes a run from a checkpoint after validating it against problem.