Probability Distribution Approach to Image Dictionaries for Compressed Sensing

2022 Fiscal Year Final Research Report

• Project/Area Number: 17K00340
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Soft computing
• Research Institution: Okayama University
• Principal Investigator: AIDA Toshiaki 岡山大学, ヘルスシステム統合科学学域, 講師 (60290722)
• Project Period (FY): 2017-04-01 – 2023-03-31
• Keywords: 圧縮センシング / 疎表現 / 辞書 / 画像修復 / 統計物理学 / 情報統計力学 / レプリカ法

Outline of Final Research Achievements

Compressed sensing enables us to infer an object even from a small number of data, if we prepare a lot of features of the object in advance. It is, in principle, the most efficient statistical inference method. However, dictionary matrices have many unknown properties, which play an essential role in the application of compressed sensing to real problems. For example, although we can understand qualitatively the optimal relation between the strength of correlation of the data and the aspect ratio of a dictionary matrix, its quantitative relation has not yet been clarified.
Since compressed sensing is mainly applied to inferring redundant data such as images, in this project, we have tried to elucidate its average performance and mechanism, taking an example of a problem to restore images degraded by Gaussian noise.

Free Research Field

機械学習，情報統計力学

Academic Significance and Societal Importance of the Research Achievements

上述の通り，圧縮センシングとは，ある条件下において，少数のデータからでも推測を可能にするもので，原理的に最も高性能な統計的推測手法である．しかし，圧縮センシングを実問題へ応用する際に本質的役割を果たす，辞書行列については不明な点が多い．本研究では，辞書行列の従う確率分布を導出した自らの研究成果を応用して，圧縮センシングの持つ高性能さの起源，特性や限界を解析的に明らかにするという学術的意義を有する．
圧縮センシングの優れた特性は，例えば，CT検査を受ける際の被曝量の低減を可能にした．従来より少数のデータからの推測が可能になれば，私達の生活にもたらす恩恵は様々な分野に及ぶことが期待される．