Development of high-efficiency calculation method for solving inverse problem and singular value decomposition for each local area in image restoration processing

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K11351
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61010:Perceptual information processing-related
• Research Institution: Shinshu University
• Principal Investigator: Shirai Keiichiro 信州大学, 学術研究院工学系, 准教授 (00447723)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 特異値分解 / 縮退処理 / カラー画像処理 / スパースモデリング

Outline of Final Research Achievements

We developed a method for efficiently calculating "small-scale but enormous amount of singular value decomposition" that appears in image signal processing, and presented the results at some domestic workshops and an international journal. This method propagates the result of singular value decomposition at a pixel to the surrounding pixels and uses it in the calculation. When this method is applied to a noise removal method, "ASTV" (Arranged Structure Tensor Total Variation), the execution time is shorten by 95% compared to the naive method without losing numerical accuracy. Additionally, when applied to the "Guided Image Filter" that is used for multipurpose processing, the execution time is shorten by 80%.

Free Research Field

画像処理

Academic Significance and Societal Importance of the Research Achievements

画像信号処理において，特異値分解は，画像中で繰り返されるパターンや，カラー画像の各色間の相関を考慮する際に用いられ，これらの保護や強調を目的とする際に，その計算過程に現れる．2010年から2015年頃に提案された画像処理法において用いられ，処理精度の向上に貢献したが，膨大な計算量，及び，分単位の処理時間を必要とする致命的な欠点があった．本手法を用いることで，その処理時間を大幅に短縮できるようになり，処理時間の面で実用には向かないと判断された手法を再利用できる可能性がある．