Approximation of a nonlinear constraint for active sonar reverberation suppression algorithm based on non-negative matrix factorization

Seokjin Lee

doi:10.7776/ASK.2026.45.3.293

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2026 Vol.45, Issue 3 Preview Page Next Page

Approximation of a nonlinear constraint for active sonar reverberation suppression algorithm based on non-negative matrix factorization 비음수 행렬 분해 기반의 능동소나 잔향 제거 알고리즘에 대한 비선형 제약 조건의 근사 기법

31 May 2026. pp. 293-304

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Abstract

In this paper, a study is conducted to improve computational complexity in order to enhance the applicability of a Non-negative Matrix Factorization (NMF)-based reverberation suppression method for the active sonar system. To deploy such methods on real hardware, computational complexity must be low; however, conventional NMF-based approaches involve exponential operations in their computational process. Since nonlinear operations such as exponential functions require relatively high computational or memory complexity when implemented on hardware, it is desirable that deployable algorithms be composed only of linear operations such as multiplication and addition. To address this issue, a new constraint formulation is derived by applying a Maclaurin approximation to the exponential function in the time-length constraint operation, and an additional method is proposed to satisfy the approximation condition by exploiting the scale ambiguity of NMF. Simulation results confirm that the proposed approximation-based method achieves performance comparable to the conventional approach, while requiring significantly reduced computation time (approximately 54.8 ms) compared to the time-length constraint using a standard exponential implementation (approximately 216.5 ms).

Keywords

Active sonar

Reverberation suppression

Non-negative Matrix Factorization (NMF)

Approximation

본 논문에서는 능동소나 시스템을 위한 비음수 행렬 분해(Non-negative Matrix Factorization, NMF) 기반의 잔향 제거 기법의 활용도를 높이기 위해 연산 복잡도를 개선하는 연구를 진행하였다. 능동소나 잔향 제거 기법을 실제 장비에 탑재하려면 연산 복잡도가 크지 않아야 하는데, 기존의 비음수 행렬 분해에 기초한 능동소나 잔향 제거 기법은 그 연산 과정이 지수함수 연산을 포함하고 있다는 문제가 있다. 지수함수와 같은 비선형 연산은 장비에 탑재할 때 상대적으로 높은 연산 복잡도 혹은 메모리 복잡도를 요구하기 때문에, 대부분의 장비 탑재 알고리즘은 가능한 곱셈 및 덧셈과 같은 선형 연산으로만 구성되는 것이 바람직하다. 본 논문에서는 이를 해결하기 위하여 시간 길이 제한 제약 조건 연산 과정의 지수함수에 매클로린 근사를 적용하여 새로운 제약 조건 연산식을 도출하였으며, 비음수 행렬 분해의 스케일 모호성을 활용하여 근사 조건을 만족시키는 방법을 추가로 도출하였다. 시뮬레이션을 통하여 제안하는 근사가 적용된 기법이 기존의 기법과 성능이 유사함을 확인하였으며, 일반적인 지수함수 구현 방법을 활용한 시간 길이 제한 제약 조건(약 216.5 ms) 대비 유의미하게 감소된 연산시간(약 54.8 ms) 이 소요됨을 확인하였다.

키워드

능동소나

잔향 제거

비음수 행렬 분해

근사

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Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 45
No :3
Pages :293-304
Received Date : 2026-03-27
Accepted Date : 2026-04-28
DOI :https://doi.org/10.7776/ASK.2026.45.3.293

The Journal of the Acoustical Society of KoreaISSN:1225-4428(Print) 2287-3775(Online)한국음향학회

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