A Study on Accuracy Improvement and Acceleration for Super-Resolution Phase Unwrapping

2018 Fiscal Year Final Research Report

• Project/Area Number: 17H07243
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Soft computing
• Research Institution: Ritsumeikan University
• Principal Investigator: Kitahara Daichi 立命館大学, 情報理工学部, 助教 (20802094)
• Research Collaborator: Hirabayashi Akira ; Yamada Isao ; Condat Laurent ; Yoshikawa Eiichi ; Kikuchi Hiroshi ; Ushio Tomoo ; Tezuka Yuji ; Iha Sanae ; Kashiwagi Atsunori
• Project Period (FY): 2017-08-25 – 2019-03-31
• Keywords: 位相アンラップ / 多項式剰余 / 部分終結式 / スプライン関数 / 超解像 / ブランチカット / 凸・非凸最適化

Outline of Final Research Achievements

For the phase unwrapping problem along the unit circle of the complex plane, we newly developed the self-reciprocal polynomial division which generates a new Sturm sequence. This Sturm sequence enables us to compute the unwrapped phase stably. Moreover, we newly defined the self-reciprocal subresultant, as the determinant of a certain matrix, and developed the relation between the signs in the Sturm sequence and those of the self-reciprocal subresultants. Then, by replacing the inductive computations of the Sturm sequence with direct numerical evaluations of the self-reciprocal subresultants, we can compute the unwrapped phase without suffering from the coefficient growth.
In APSIPA 2018, for the 180-degree ambiguity resolution of a two-dimensional vector field, we proposed a branch cut type solver which is inspired by Goldstein’s approach for 2D phase unwrapping. In ICASSP 2019, for 2D phase unwrapping problem, we showed the effectiveness of a new convex relaxation formulation.

Free Research Field

工学

Academic Significance and Societal Importance of the Research Achievements

自己反転型多項式除算によって剰余体などの代数系を定義できれば，符号理論や多項式代数の分野で新たな理論が展開できる可能性がある．また，工学的にも，2次元位相アンラップ法の高精度化やブランチカット型符号推定法の開発により，「合成開口レーダ・ソナーによる地形・海底観測」，「光学式干渉計による精密な3次元形状計測」，「MRIや位相コントラストX線CTによる医療診断」など様々なセンシング技術の精度向上が期待できる．