neural-phase-correlation

name	neural-phase-correlation
description	Learned generalization of phase correlation that lifts the fixed Fourier basis restriction to discover unknown transformations between observations. Applicable to image registration, non-rigid deformation, and quantum Hamiltonian eigenstate recovery from observation pairs.
metadata	{"arxiv_id":"2606.18496","published":"2026-06-16","authors":"Cole Reynolds","tags":["phase-correlation","neural-networks","image-registration","quantum","fourier","correspondence"]}

Neural Phase Correlation

Description

A learned generalization of phase correlation that lifts the fixed Fourier basis restriction, enabling discovery of unknown transformations between observations. Extends from global translation to dense non-rigid deformations and unitary dynamics. Validated on cardiac MRI, echocardiography, and quantum harmonic oscillator eigenstate recovery.

Activation Keywords

• neural phase correlation
• learned phase correlation
• image registration neural
• fourier correspondence
• transformation discovery
• quantum eigenstate recovery
• 相位相关学习

Core Concepts

Phase Correlation Generalization

• Classical limitation: Standard phase correlation only measures global translation via fixed Fourier basis
• Key insight: Learn the basis on which the transformation decomposes, rather than using fixed Fourier modes
• Algebraic primitive: Same mathematical foundation extends to dense non-rigid deformations and unitary dynamics
• First-class transformation: Architecture represents transformation as explicit object, not implicit through similarity functions

Applications

1. Medical imaging registration: ACDC cardiac MRI, CAMUS echocardiography
2. Quantum physics: Recovering Hamiltonian eigenstates from observation pairs
3. Non-rigid deformation: Dense correspondence beyond global translation

Usage Patterns

Pattern 1: Image Registration

When registering medical images or general observation pairs:

1. Encode both observations into shared representation
2. Apply learned phase correlation in Fourier-like domain
3. Decode transformation from correlation peak
4. Achieves state-of-the-art without auxiliary scoring mechanisms

Pattern 2: Quantum State Analysis

When analyzing quantum systems from observation data:

1. Apply to pairs of time-evolved wavefunctions
2. Framework recovers Hermite-function eigenstates
3. Quantized energy levels extracted from observation pairs alone
4. No prior knowledge of Hamiltonian required

Pattern 3: Non-rigid Deformation Tracking

When tracking dense non-rigid deformations:

1. Same algebraic primitive extends beyond translation
2. Learns basis for deformation decomposition
3. Matches/exceeds prior baselines on cardiac benchmarks

Methodology

Step 1: Representation Learning

• Learn the decomposition basis from data
• Same architecture handles translation, deformation, and unitary dynamics

Step 2: Correlation Computation

• Apply phase-correlation algebraic primitive on learned basis
• Extract transformation parameters from correlation structure

Step 3: Validation

• Evaluate on paired observations
• For quantum systems: verify eigenstate and energy recovery

Error Handling

Mode Collapse in Learned Basis

• Ensure basis diversity through regularization
• Validate against known ground-truth transformations

High-Frequency Artifacts

• Apply appropriate filtering in learned frequency domain
• Balance resolution with noise robustness

Examples

Example: Quantum Harmonic Oscillator

Applied to time-evolved wavefunction pairs of 1-D quantum harmonic oscillator, the framework recovers Hermite-function eigenstates and quantized energy levels from observation pairs alone — no Hamiltonian specification needed.

Resources

• arXiv: 2606.18496 - "Neural Phase Correlation"
• Related: quantum-state-engineering, quantum-brain-modeling