Study On Adaptive Sparse Filtering For Fringe Patterns

Optical measurement interference technology has a wide application in sci-entific research and engineering practice. In the process of imaging,because of the limitation of the imaging conditions and the methods, all kinds of random noise and blur influence the technical validity and accuracy. It has always been a key issue and hotspot that to to achieve the accurate measurement and identification by restoring and enhancing image which contains different directions and frequencies.In the processing of removing the noise and all kinds of interference of the fringe pattern, we cannot be clearly separated the fringe pattern and the noises as the instability of fringe pattern and the frequency of the fringe pattern and the noises often overlap together; The simple processing will dim the characteristic of the fringe pattern, especially for the high frequency of fringe pattern. For example, the mean filter,median filter,wavelet threshold denoising and so on. Spin filtering, STFT, Goldstein filter and Gabor filter consider the non-stationary characteristics of fringe pattern, feasible results are obtained. But they can’t meet the high accuracy of the practical engineering.Image sparse filtering methods enhance the images by using their sparse characteristics. It has a great influence. At present,the research about the image sparse representation goes along two lines in general.(1) The multi-scale geometric analysis based on the fixed base function. For example, all kinds of fourier transform methods and wavelet transform method. Through fitting local geometrical structure of the image, these kinds of methods can obtain the image sparse representation.(2)The theory of a sparse representation based on the complete dictionary. These kinds of methods get the learned dictionary by learning from some of the samples. The basic functions is adaptively got according to the image itself, so we can get the image sparse representation and they have stronger adaptive abilities. But the computational efficiency is low and the algorithm is not quick enough for the image.In this paper, the fringe pattern is divided into several overlapping small pieces.We use sparse representation for the each pieces, and filtering through the adaptive weighted matching. Specifically, two aspects has been carried on the thorough research in this paper:(1)Block DCT filter based on self-adaption. DCT filtering algorithm have a hypothesis:the image is stable. But the fringe pattern is complex and changeable, a fully stable image is rare. Using fixed hard threshold processing on the whole image, denoising effect would be insufficient or dim the charac-teristics. Each small piece is stable when we divide the image into pieces. In each pieces, we use different threshold and adaptive weighted matching. We get a good result.(2) Short-time fourier filter based on self-similarity. The short-time fourier filtering algorithm is better to adapt to not stability than fourier transform. First, we divide the image into the overlapping pieces and use fourier filtering for each pieces; By extracting specific frequency of the image through fourier inverse transform, we get the special frequency image. Second, due to the characteristics of the special frequency image is consistent, there is a great deal of redundant information, we use the Non-local means for denoising. Finally,we add up all the special frequency image, and the filtering result is obtained.The characteristics of the fringe pattern is very self-similarity and redun-dancy, so it has sparse decomposition coefficient under the image transforma-tion, but the noise is not so. We make full use of the sparse, and get a good result. It can satisfy the requirement of the high precision optical measurement and has important scientific value and practical significance.