EigenDenoise

A native macOS application for image denoising and spectral analysis based on random matrix theory (RMT). Pure-Swift, Metal-accelerated, App Store sandbox-ready.

What it does

Two complementary RMT-based denoisers run on the same noisy image stack, side-by-side with three interactive tabs that visualise the underlying mathematics:

• Marchenko–Pastur thresholding — classical singular-value cutoff at the bulk edge (1 + √y)·√(λ_p/q), using the spread rule from the batch MPPCA literature.
• Generalized-covariance oracle — models the bulk via the limiting spectral density of B_n = S_n T_n with two-point spike weight H = β·δ_a + (1−β)·δ_1. Best (a, β) is found by differential evolution against a held-out clean reference.
• Spectral visualisations — Eigenvalue distribution (Monte-Carlo histogram + closed-form F_{y,H}(z) overlay + Case 1/2/3 support edges), Im(s) vs z (Stieltjes-transform imaginary part), Roots vs β (cubic-root behaviour over the spike fraction).

Features

• Five noise models — Gaussian, Mixture-of-Gaussians, Two-Point H, Half-Gaussian, Block-Half. Seedable for reproducibility.
• Curated dataset gallery — one-click downloads in the Datasets tab:
  • ORL (AT&T) Faces — 400 PGMs
  • CBSD68 — 68 colour Berkeley test images
  • Brain Tumor MRI — 3,264 T1 slices (live GitHub listing)
  • Custom URL lists with per-image checkboxes and destination preview
• Metal GPU acceleration — MPSMatrixMultiplication for the Gram step on Apple Silicon, transparent Accelerate (BLAS / LAPACK) fallback. Eigen-decomposition uses LAPACK dsyevd.
• Sandboxed storage — datasets save to your sandboxed Application Support folder by default; pick any local folder via security-scoped bookmark and the choice persists across launches.
• No telemetry, no analytics, no sign-in — all computation is local; network is touched only when you explicitly click a preset or paste URLs and press Download.

Build

Requires Xcode 15.4+ on macOS 14 (Sonoma) or later.

git clone https://github.com/yu314-coder/EigenDenoise.git
cd EigenDenoise
open EigenDenoise.xcodeproj
# ⌘R

There are no external Swift package dependencies — Charts and SwiftUI ship with the OS. The project targets arm64 (Apple Silicon) and works under Rosetta on Intel; Metal acceleration falls back to Accelerate when no Metal device is present.

Layout

EigenDenoise/
├── EigenDenoise.xcodeproj/
├── EigenDenoise/
│   ├── EigenDenoiseApp.swift       @main + menu commands
│   ├── ContentView.swift
│   ├── EigenDenoise.entitlements   App Sandbox = YES
│   ├── Math/                       RMT, Eigh, MetalCompute, SpectralDensity, …
│   ├── Denoise/                    NativeDenoise, NoiseInjection, ImageIO, …
│   ├── UI/                         AppModel, FolderView, DenoiseView, …
│   └── Assets.xcassets/
├── icons/
└── scripts/

Mathematics in brief

For X ∈ ℝ^{p×n} with i.i.d. N(0, 1) entries, S_n = (1/n) X Xᵀ and T_n = diag(t₁,…,t_p) with empirical distribution F^{T_n} ⇒ H = β·δ_a + (1−β)·δ_1, the generalized sample covariance matrix is B_n = S_n T_n. Its Stieltjes transform s(z) satisfies the cubic

a·z·s³ + (a(z − y + 1) + z)·s² + (a + z − y + 1 − y·β·(a − 1))·s + 1 = 0

with concentration ratio y = p / n. The closed-form limiting density f_{y,H}(z) follows from Cardano's depressed-cubic root, and the support is recovered from the bulk-edge function g(t) plus the discriminant of the quartic P_4(t) for one-interval (Cases 1, 3) vs two-interval (Case 2) topology. Both are implemented in Math/SpectralDensity.swift.

License

MIT — see LICENSE.

Author

Yao-Hsing Yu · euler.yu@gmail.com · @yu314-coder