Journal of the Institute of Electronics and Information Engineers (전자공학회논문지)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Missing Data Correction and Noise Level Estimation of Observation Matrix

관측행렬의 손실 데이터 보정과 잡음 레벨 추정 방법

  • Received : 2015.11.07
  • Accepted : 2016.03.04
  • Published : 2016.03.25
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Abstract

In this paper, we will discuss about correction method of missing data on noisy observation matrix and uncertainty analysis for the potential noise. In situations without missing data in an observation matrix, this solution is known to be accurately induced by SVD (Singular Value Decomposition). However, usually the several entries of observation matrix have not been observed and other entries have been perturbed by the influence of noise. In this case, it is difficult to find the solution as well as cause the 3D reconstruction error. Therefore, in order to minimize the 3D reconstruction error, above all things, it is necessary to correct reliably the missing data under noise distribution and to give a quantitative evaluation for the corrected results. This paper focuses on a method for correcting missing data using geometrical properties between 2D projected object and 3D reconstructed shape and for estimating a noise level of the observation matrix using ranks of SVD in order to quantitatively evaluate the performance of the correction algorithm.

본 논문에서는 잡음이 내포된 관측행렬에서 손실 데이터를 보정하는 방법과 그 잠재적 잡음에 대한 불확실성 분석에 대해서 다룰 것이다. 관측행렬에 잡음과 손실 데이터가 없을 경우는 SVD 행렬인수분해 방법에 의해 정확한 복원 결과를 얻을 수 있다. 그렇지만 일반적으로 관측행렬의 일부 요소는 손실되거나 잡음 영향을 받게 된다. 이러한 경우는 3차원 복원 오차를 유발시킬 뿐만 아니라 그 해결책 또한 찾기가 쉽지 않은 문제가 있다. 따라서 3차원 복원 오차를 최소화하기 위해서는 무엇보다도 잡음 환경에서 손실 데이터를 신뢰성 있게 보정하고, 그 보정된 결과를 정량적으로 평가를 해줄 필요가 있다. 본 논문은 2차원 투영 객체와 3차원 복원 형상 사이의 기하학적 특성을 이용해 손실 데이터를 보정 하는 방법을 소개하고, 그 보정 성능을 정량적으로 평가할 수 있는 SVD rank이론을 이용한 관측행렬의 잡음 레벨 추정 방법에 대해서 제안할 것이다.

Keywords

References

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