Batch & CUDA

Batch API (CPU and Generic Arrays)

Use solve_batch for input arrays shaped:

(spatial_dim_1, spatial_dim_2, ..., spatial_dim_k, batch)

The last axis is treated as batch index, and TV operators are applied only across spatial axes.

Example:

u_batch, stats = TotalVariationImageFiltering.solve_batch(
    f_batch,
    TotalVariationImageFiltering.ROFConfig();
    lambda = 0.1,
    tv_mode = TotalVariationImageFiltering.IsotropicTV(),
)

For PDHG batch solves, you can additionally pass:

• constraint = TotalVariationImageFiltering.NonnegativeConstraint(), or
• constraint = TotalVariationImageFiltering.BoxConstraint(lower, upper).

Batch state reuse:

• pass state = [ROFState(slice1), ROFState(slice2), ...] for ROF;
• pass state = [PDHGState(slice1), PDHGState(slice2), ...] for PDHG.

State vector length must match batch size.

CUDA Extension

The extension module TotalVariationImageFilteringCUDAExt is loaded automatically when:

• CUDA.jl is installed and loaded,
• a functional CUDA runtime/device is available.

Example:

using CUDA
using TotalVariationImageFiltering

f_gpu = CUDA.rand(Float32, 256, 256)
problem_gpu = TotalVariationImageFiltering.TVProblem(f_gpu; lambda = 0.15f0)
u_gpu, stats_gpu = TotalVariationImageFiltering.solve(problem_gpu, TotalVariationImageFiltering.ROFConfig())

CUDA Coverage

Current behavior based on extension code/tests:

• CUDA kernels are provided for gradient/divergence/projection primitives.
• Single-image ROF and PDHG on CuArray are supported.
• Batched CUDA solve is specialized for ROFConfig and PDHGConfig.
• Batched CUDA path currently requires:
  • L2Fidelity (ROF), or L2Fidelity / PoissonFidelity (PDHG),
  • Neumann boundary.

ROF paths currently support only constraint = NoConstraint().

If CUDA is unavailable, CPU paths continue to work.

Numerical Equivalence Checks

Repository tests compare CPU and CUDA outputs with tolerances for:

• single-image ROF solve;
• batched ROF solve.