Interactive Medical Imaging Simulator: Wiener Filter Denoising & MATLAB Tutorial

Interactive Medical Imaging Simulator

Adjust the scanner parameters to see how the 32x32 CIR knowledge restores the 128x128 patient scan.

Signal-to-Noise Ratio (SNR): 30 dB

Hardware Blur (Sigma): 1.2

32x32 Pilot Calibration

128x128 Raw Scan

Wiener Reconstruction

> System Standby... Ready for Calibration.

Mathematical Theory & Simulation Logic

The simulation follows a Two-Phase Stochastic Process that mimics real-world MRI and 5G communication systems. Here is the mathematical bridge between the domains:

Phase I: Time-Domain Distortions

In the spatial (time) domain, the patient image \(s[n]\) is convolved with the Channel Impulse Response \(h[n]\) and corrupted by additive white noise \(v[n]\):

$$y[n] = (s * h)[n] + v[n]$$

The simulation models the Quantum Mottle as signal-dependent noise, where the variance is scaled by the target SNR defined in the slider.

Phase II: Frequency-Domain Deconvolution

To avoid the extreme computational cost of spatial deconvolution, we move to the Frequency Domain via the Fast Fourier Transform (FFT). Convolution becomes simple multiplication:

$$Y(u,v) = S(u,v) \cdot H(u,v) + V(u,v)$$

Phase III: The LMMSE (Wiener) Optimal Estimator

The simulator uses the 32x32 Pilot Knowledge to estimate \(\hat{H}\). However, direct inversion (\(1/H\)) would explode the noise. We apply the Wiener Regularization:

The Reconstruction Equation: $$\hat{S}(u,v) = \left[ \frac{H^*(u,v)}{|H(u,v)|^2 + K} \right] \cdot Y(u,v)$$

Where \(K = 1/SNR\). When noise is high, the filter smoothly attenuates frequencies instead of amplifying error.

Get MATLAB Code →

Online Simulations Main Page →