ComfyUI Compressed Sensing Node

A custom ComfyUI node that reconstructs an image from only 10% randomly sampled k-space (Fourier) coefficients using rigorous Compressed Sensing theory.

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Algorithm

1. Measurement — k-space subsampling

The image is transformed into the 2-D Fourier (k-space) domain, and only 10% of the complex coefficients are retained:

y = Ω ⊙ Fx

| Symbol | Meaning | |--------|---------| | x | Original image | | F | 2-D orthonormal DFT (numpy.fft.fft2, norm='ortho') | | Ω | Binary k-space sampling mask (10% ones) | | y | Observed k-space measurements |

Using the Fourier domain satisfies the incoherence condition central to CS theory: the DFT basis is maximally incoherent with the canonical (pixel) basis, and natural images have sparse gradients (TV sparsity), giving theoretical recovery guarantees.

2. Reconstruction — ISTA with TV regularisation

The image is recovered by solving the convex optimisation problem:

min_x  ½‖Ω ⊙ (Fx − y)‖²  +  λ·TV(x)

Solved iteratively via ISTA (Iterative Shrinkage-Thresholding Algorithm):

∇f(x) = F^H [ Ω ⊙ (Fx − y) ]          ← gradient of data-fidelity
       = IFFT2( Ω ⊙ (FFT2(x) − y) ).real

x ← prox_{λ·TV}( x − ∇f(x) )           ← TV proximal step (Chambolle)

The step size is exactly 1 because F is unitary (F^H F = I) and Ω is a binary mask, so the Lipschitz constant of the forward operator is L = 1.

Why k-space, not pixel-domain?

| Property | Pixel-domain sampling | k-space sampling (this node) | |----------|----------------------|----------------------------------| | Measurement domain | Pixel space | Fourier space | | Sparsity domain | Gradient (TV) | Gradient (TV) | | Incoherence | Weak (same domain) | Strong (maximally incoherent) | | CS theory guarantee | Limited | Satisfies RIP w.h.p. | | Real-world analogue | — | MRI, radar |

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Sampling Patterns

variable_density (default, MRI-style)

Samples more densely near DC (low frequencies) using a 2-D Gaussian density. DC is always included. Gives better perceptual quality because most image energy is at low frequencies.

uniform

Uniformly random k-space subsampling. Theoretically cleaner (i.i.d. draws), useful for benchmarking.

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Installation

# 1. Copy this folder into ComfyUI's custom_nodes directory
cp -r ComfyUI_CompressedSensing /path/to/ComfyUI/custom_nodes/

# 2. Install dependencies
pip install scikit-image

# 3. Restart ComfyUI

numpy and torch are already bundled with ComfyUI. scikit-image is strongly recommended for faster TV denoising. A pure-NumPy Chambolle fallback is included if it is unavailable.

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Node Reference

Category: CompressedSensing Node name: Compressed Sensing (10% Random Sampling)

Inputs

| Name | Type | Default | Description | |------|------|---------|-------------| | image | IMAGE | — | Input image | | sampling_ratio | FLOAT | 0.10 | Fraction of k-space to observe (0.01 – 1.00) | | sampling_pattern | ENUM | variable_density | variable_density or uniform | | iterations | INT | 300 | ISTA iteration count. More = better quality, slower | | tv_weight | FLOAT | 0.05 | TV regularisation strength λ. Lower = sharper; higher = smoother | | seed | INT | 0 | Random seed. 0 = different mask every run |

Outputs

| Name | Type | Description | |------|------|-------------| | reconstructed | IMAGE | CS-reconstructed image | | kspace_mask | IMAGE | k-space sampling pattern (DC at centre, white = sampled) |

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Parameter Tuning Guide

| Goal | Suggestion | |------|-----------| | Better quality | Increase iterations (500 – 1000) | | Sharper edges | Decrease tv_weight (0.01 – 0.03) | | Smoother result | Increase tv_weight (0.1 – 0.3) | | Reproducible mask | Set seed to any fixed non-zero integer | | More measurements | Increase sampling_ratio (0.20 – 0.30) |

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Example Workflow

Load Image → CompressedSensing → Preview Image  (reconstructed)
                               → Preview Image  (kspace_mask)

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Requirements

• Python 3.8+
• numpy
• torch (provided by ComfyUI)
• scikit-image ≥ 0.19 (recommended)

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Theoretical Background

Compressed Sensing (Candès, Romberg & Tao 2006; Donoho 2006) states that a signal with a sparse representation in basis Ψ can be exactly recovered from m = O(s log n) incoherent measurements — far fewer than the n samples Nyquist requires — where s is the sparsity level.

This node's setup:

| CS ingredient | Choice | |---------------|--------| | Signal | Natural image x ∈ ℝⁿ | | Sparsifying basis Ψ | Gradient domain (TV) | | Measurement matrix Φ | Subsampled 2-D DFT | | Incoherence μ(Φ, Ψ) | Near-minimal (Fourier ↔ pixel) | | Recovery algorithm | ISTA (convex, globally convergent) |

Lustig, Donoho & Pauly (2007) "Sparse MRI" is the seminal paper applying exactly this approach to accelerate MRI acquisition.

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License

MIT