ANNI: Auditory Nerve Noticeability Index

ANNI is a full-reference measure of how noticeable the difference between a reference and a test audio signal is. It simulates how the auditory nerve responds to each signal and compares the two responses the way an ideal observer would. The score is in d′ units, the standard unit of detectability: 0 means no difference, and larger values mean a more noticeable difference. ANNI is built for small differences near the threshold of hearing, such as audio watermarks.

Status: research prototype (v0.1). ANNI is calibrated so that D = 1 marks a just-noticeable difference: the point at which listeners in classic laboratory experiments start to detect a change. A score below 1 should therefore mean the difference is hard to hear, even when comparing directly. This has not yet been confirmed by listening tests on real-world audio.

Install

pip install deepmark-anni

Requires Python 3.9 or newer, PyTorch, NumPy and soxr.

For development, install from a clone in editable mode:

git clone https://github.com/deepmark/anni.git
cd anni
python -m pip install -e ".[test]"

Usage

import soundfile as sf          # any audio loader works
from anni import ANNI

reference, sr = sf.read("original.wav")
test, _ = sf.read("watermarked.wav")

anni = ANNI()
anni(reference, test, sr=sr)
# e.g. {'D_peak': 1.49, 'D_med': 0.81}

Lower is better. To compare two processed versions, score both against the same reference. A difference between two scores can be expressed in dB as 20·log₁₀(D_B / D_A).

Inputs

• Mono signals at the same sample rate. The model runs at 44.1 kHz; other rates are resampled to it.
• Playback level: the reference is played at 65 dB SPL, about conversational speech (ANNI(level=...) changes this). Both signals get the same gain, so a level change in the test signal counts as a difference.
• Timing: a constant delay of up to ±10 ms is removed. If the lengths differ, the longer signal is cut.
• Length: at least 0.5 s; typical test clips are about 10 s long, as for PESQ and ViSQOL. A 5 s pair takes about 1 s and 0.9 GB on a laptop CPU. Long files are processed in blocks, so memory grows only slowly with length (2 min: about 20 s and 1.2 GB). On an NVIDIA GPU, use ANNI(device="cuda").

ANNI warns whenever it changes the inputs (resampling, cutting, removing a delay or a constant offset between them) and when the test signal is polarity-inverted. It also warns when the two signals correlate weakly (below 0.9), for example after a speech codec: the scores may then not be meaningful.

How it works

1. A filter models the outer and middle ear.
2. An auditory-nerve model turns each signal into the firing rates of 128 nerve fibres tuned from 80 Hz to 16 kHz: cochlear (gammatone) filters, inner-hair-cell rectification and smoothing, and a sigmoid firing-rate curve.
3. Two observers compare the firing rates. Each change is weighed against the natural randomness of nerve firing, which is what makes loud sounds mask quieter ones. One observer looks at slow changes in firing rate (level and colouration), the other at changes in how the rate fluctuates (roughness, flutter).
4. The evidence is added up over fibres and over 200 ms windows. D_peak is the largest window, D_med the median.

Four constants set the scale so that classic laboratory thresholds score about D = 1: the threshold of hearing and the 1 dB level difference at 1 kHz (following Taal et al. 2012), noise and tone masking (ITU-R BS.1387), and amplitude-modulation detection on tones (He et al. 2008) and on noise (O'Connor et al. 2011).

A function-by-function walk-through of the code is in docs.md. For a comparison with PESQ and ViSQOL on controlled changes, with audio, see examples/.

Evaluation

On ODAQ, an open dataset of music, film sound and speech over music rated by 26 listeners (210 versions of 30 excerpts; Torcoli et al. 2024), D_med orders the versions like the listeners with a Spearman correlation of 0.85 (95 % interval 0.79–0.89). That is on par with Zimtohrli (0.83) and above ViSQOL (0.65 in audio mode) and PESQ (0.42). On degraded speech, in the TCD-VoIP dataset (Harte et al. 2015; packet loss, clipping, echo, competing speakers and noise, rated by 24 listeners), PESQ and ViSQOL follow listeners better.

Limitations

• It compares the signals moment by moment, so it does not suit audio whose timing or pitch has changed (time-stretching, pitch-shifting) or that went through a speech codec.
• It doesn't see energy above 16 kHz or below 80 Hz, very fast fluctuations or fine timing structure.
• Mono only, normal hearing.

Credits and licence

ANNI is developed by DeepMark Inc. and released under the MIT License.

The auditory-nerve model is adapted from Mark R. Saddler's auditory_machine_learning. If you use ANNI, please also cite:

• Saddler, M. R., & McDermott, J. H. (2024). Models optimized for real-world tasks reveal the task-dependent necessity of precise temporal coding in hearing. Nature Communications. doi:10.1038/s41467-024-54700-5

Listening-test data:

• Torcoli, M., Wu, C.-W., Dick, S., Williams, P. A., Halimeh, M. M., Wolcott, W., & Habets, E. A. P. (2024). ODAQ: Open Dataset of Audio Quality. Proc. IEEE ICASSP. arXiv:2401.00197
• Harte, N., Gillen, E., & Hines, A. (2015). TCD-VoIP, a research database of degraded speech for assessing quality in VoIP applications. Proc. QoMEX.

Calibration references:

• Taal, C. H., Hendriks, R. C., & Heusdens, R. (2012). A low-complexity spectro-temporal distortion measure for audio processing applications. IEEE Transactions on Audio, Speech, and Language Processing, 20(5). doi:10.1109/TASL.2012.2184753
• ITU-R BS.1387: Method for objective measurements of perceived audio quality (PEAQ).
• He, N., Mills, J. H., Ahlstrom, J. B., & Dubno, J. R. (2008). Age-related differences in the temporal modulation transfer function with pure-tone carriers. The Journal of the Acoustical Society of America, 124(6), 3841–3849. doi:10.1121/1.2998779
• O'Connor, K. N., Johnson, J. S., Niwa, M., Noriega, N. C., Marshall, E. A., & Sutter, M. L. (2011). Amplitude modulation detection as a function of modulation frequency and stimulus duration: comparisons between macaques and humans. Hearing Research, 277, 37–43. doi:10.1016/j.heares.2011.03.014