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Griffin-Lim Algorithm

introduced 1984 75 papers tagged archive 2025-07-28

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

The Griffin-Lim Algorithm (GLA) is a phase reconstruction method based on the redundancy of the short-time Fourier transform. It promotes the consistency of a spectrogram by iterating two projections, where a spectrogram is said to be consistent when its inter-bin dependency owing to the redundancy of STFT is retained. GLA is based only on the consistency and does not take any prior knowledge about the target signal into account.

This algorithm expects to recover a complex-valued spectrogram, which is consistent and maintains the given amplitude 𝐀, by the following alternative projection procedure:

𝐗^([m+1]) = P_𝒞(P_𝒜(𝐗^([m])))

where 𝐗 is a complex-valued spectrogram updated through the iteration, P_𝒮 is the metric projection onto a set 𝒮, and m is the iteration index. Here, 𝒞 is the set of consistent spectrograms, and 𝒜 is the set of spectrograms whose amplitude is the same as the given one. The metric projections onto these sets 𝒞 and 𝒜 are given by:

P_𝒞(𝐗) = 𝒢𝒢^†𝐗 P_𝒜(𝐗) = 𝐀 ⊙𝐗 ⊘|𝐗|

where 𝒢 represents STFT, 𝒢^† is the pseudo inverse of STFT (iSTFT), ⊙ and ⊘ are element-wise multiplication and division, respectively, and division by zero is replaced by zero. GLA is obtained as an algorithm for the following optimization problem:

min_𝐗 || 𝐗 - P_𝒞(𝐗) ||²_(Fro) s.t. 𝐗 ∈𝒜

where || · ||_(Fro) is the Frobenius norm. This equation minimizes the energy of the inconsistent components under the constraint on amplitude which must be equal to the given one. Although GLA has been widely utilized because of its simplicity, GLA often involves many iterations until it converges to a certain spectrogram and results in low reconstruction quality. This is because the cost function only requires the consistency, and the characteristics of the target signal are not taken into account.

Papers archive 2025-07-28

30 shown of 75, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 55 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
Speech Synthesis45
Text to Speech44
text-to-speech44
Text-To-Speech Synthesis15
Decoder10
Sentence6
Speech Recognition5
Transfer Learning5
Voice Cloning5
Audio Synthesis4
GPU4
Voice Conversion4
speech-recognition4
Data Augmentation3
Expressive Speech Synthesis3
Generative Adversarial Network3
Speaker Verification3
All2
Automatic Speech Recognition2
Automatic Speech Recognition (ASR)2

Usage over time archive 2025-07-28

Papers per year tagged with Griffin-Lim Algorithm: 2017 to 2024, peak 19 19 0 2017: 5 papers 2017 2018: 7 papers 2018 2019: 7 papers 2019 2020: 19 papers 2020 2021: 14 papers 2021 2022: 10 papers 2022 2023: 7 papers 2023 2024: 6 papers 2024
Papers per year the archive tags with this method, by the paper's archive date (75 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Phase Reconstruction

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