phase-retrieval

Phase retrieval IS a specific kind of algorithm: it is an iterative computational procedure (e.g. Gerchberg-Saxton, hybrid input-output) that recovers phase from magnitude-only data. Specific→general per Law 9.

Fourier transform (1822) predates phase retrieval methods by over a century. Phase retrieval algorithms (Gerchberg-Saxton 1972, hybrid input-output) fundamentally depend on the Fourier transform as their core computational operation — they iterate FFT/IFFT to recover missing phase from magnitude data. Remove the Fourier transform and phase retrieval has no mathematical machinery to operate on. Which-came-first: fourier-transform is older and fed into phase-retrieval.

Phase retrieval recovers phase from magnitude-only spectral data. Remove the magnitude spectrum and phase retrieval has no input to operate on. The removal test is satisfied: without magnitude spectra, phase retrieval cannot function.

Phase retrieval as a computational technique requires the Fourier transform to operate — it works by manipulating phase and magnitude in the frequency domain. Remove the Fourier transform and phase retrieval has no mathematical framework to function. The removal test is constitutive.

Phase retrieval algorithms operate on magnitude spectrograms produced by STFT; without STFT analysis there is no input representation for retrieval.

Phase retrieval reconstructs phase from magnitude spectrograms to restore perceptual quality of speech signals. It is built for the purpose of serving speech enhancement, servant points at master per Law 8d.

Phase retrieval is a specific signal processing problem class concerned with reconstructing a signal from magnitude information alone. A competent speaker would call phase retrieval a kind of signal processing technique. Law 9 specific→general.

Griffin-Lim IS a specific kind of phase-retrieval: it is a concrete algorithm for recovering missing phase information from a magnitude spectrogram. A competent speaker would call Griffin-Lim a phase-retrieval algorithm. Nearest kind: phase-recovery and iterative-algorithm do not exist, so phase-retrieval is the nearest kind.

phase-retrieval as a general mathematical problem (reconstructing signals from magnitude-only measurements) predates and generalizes the Griffin-Lim algorithm. Griffin-Lim is a specific iterative algorithm developed within the phase-retrieval domain. Which-came-first test: phase-retrieval concept existed first, Griffin-Lim algorithm was developed as a method to solve it.

Phase estimation is a specific technique for recovering phase information from measurements — it is a case of the broader phase retrieval problem. A competent speaker would call phase estimation 'a phase retrieval method.' Nearest kind is phase-retrieval.

Phase retrieval as a problem domain predates the Griffin-Lim algorithm. Griffin-Lim is a specific solution that came later, building on the established concept of recovering phase from magnitude information.

Griffin-Lim IS a specific algorithm for the phase retrieval problem — recovering phase from magnitude information. A competent speaker would call it 'a phase retrieval algorithm.' Files against the nearest kind per Law 9.

Griffin-Lim iterative algorithm is designed and maintained specifically to perform phase retrieval from magnitude spectrograms. Its purpose is phase retrieval.

Phase-unwrapping is designed and maintained for the purpose of recovering continuous phase, which is a core operation in phase-retrieval workflows. Its intended purpose is to enable phase retrieval from wrapped measurements.