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Percent Root-mean-square Difference (PRD)

Key: prd · Family: signal fidelity · Better: lower ↓ · Per-lead: yes

PRD asks: how large is the point-by-point error compared with the size of the real signal? It comes from ECG compression, where it measures how much a compressed signal deviates from the original.

Try it

The shaded area is the point-wise error between a real beat and its synthetic nearest neighbour. All five point-wise metrics are shown; PRD is highlighted.

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What to notice:

  • 20 ms late: a small timing shift of a perfect beat gives a large PRD, because the sharp R peak no longer overlaps. Point-wise metrics punish phase shifts hard; see DTW for a shift-tolerant alternative.
  • Baseline drift adds error everywhere, even though the beat shape is perfect.
  • Amplitude changes scale the error directly.

How it works

  1. For each real recording (up to n_subsample), find the nearest synthetic recording: the one with the smallest Euclidean distance over all leads jointly.
  2. For each lead, compute PRD between the real recording and that neighbour.
  3. Average over recordings; the score is the mean over leads.

Because generated ECGs are not paired with real ones, the nearest-neighbour match finds the synthetic ECG that best explains each real ECG.

The math

\[ \mathrm{PRD} = 100 \cdot \frac{\lVert x_r - x_s \rVert_2}{\lVert x_r \rVert_2} = 100\cdot\sqrt{\frac{\sum_t (x_r[t]-x_s[t])^2}{\sum_t x_r[t]^2}} \]

Reading the score

  • 0 % is a perfect match. In compression work, PRD below about 9 % is often called "good" quality. Generated ECGs are rarely that close, so compare against a real-vs-real baseline.
  • The denominator includes the DC level: a signal with a baseline offset has a larger \(\lVert x_r\rVert\), so PRD depends on preprocessing. Some papers use a mean-removed variant (PRDN).
  • PRD rewards a close look-alike for each real ECG. It says nothing about whether the synthetic set is diverse or realistic overall; use it with a distribution metric.

Use it with ECGEN-Eval

ecgen-eval eval --real real.npy --synthetic synth.npy -m prd --output report.html

from ecgen_eval import load_ecg_npy, AVAILABLE_METRICS

real = load_ecg_npy("real.npy", fs=500)
synth = load_ecg_npy("synth.npy", fs=500)

result = AVAILABLE_METRICS["prd"](n_subsample=500).compute(real.data, synth.data, lead_names=real.lead_names)
print(f"PRD = {result.score:.1f} %")

Parameters are in the Metric Reference.

Learn more

  • Zigel, Cohen & Katz, The weighted diagnostic distortion (WDD) measure for ECG signal compression, IEEE TBME 2000.
  • Related point-wise metrics: MAE, PSNR, SSIM.