Shear Wavelet Frame Transform and Its Applications

Abstract

이 논문은비 등방성웨이블릿변환과그 응용에대해서다룬다.이변환은 일종의방향성웨이블릿변환으로이미지의모서리같은비등방성기능들을 분석할 수 있다. 웨이블릿 변환에 방향성을 부여하기 위하여 연속 웨이블릿 변환에 쉬어 행렬을 이용하였다. 이 연속 쉬어 변환에서 쉬어 프레임을 만들 고 다시 방향성을 가진 고정된 이산 변환을 정의하여 여러 이미지들의 노이 즈 제거 등을 통해 기존의 웨이블릿 변환들과 비교하였다. 또한 BM3D와 비 등방성 웨이블릿 변환을 결합하여 개선된 노이즈 제거 효과를 확인하였다.|This thesis describes the shear wavelet frame transform(SWFT) and its ap- plications. SWFT is designed for one of the directional wavelet transform. By using it we can analyze anisotropic features such as edges in images. To give the directionality we use a shear matrix for the continuous wavelet transform. In the first part, we review the wavelet frame and the stationary wavelet trans- form. And we design the shear wavelet frame transform and its inverse trans- form. In the later part we review MMSE and BM3D as denoising schemes. A range of examples illustrate the better performance of this SWFT in denosing compared with DWT, SWT and WMSAD. We also propose another algorithm that combining SWFT and BM3D which improves the performance beyond BM3D.; This thesis describes the shear wavelet frame transform(SWFT) and its ap- plications. SWFT is designed for one of the directional wavelet transform. By using it we can analyze anisotropic features such as edges in images. To give the directionality we use a shear matrix for the continuous wavelet transform. In the first part, we review the wavelet frame and the stationary wavelet trans- form. And we design the shear wavelet frame transform and its inverse trans- form. In the later part we review MMSE and BM3D as denoising schemes. A range of examples illustrate the better performance of this SWFT in denosing compared with DWT, SWT and WMSAD. We also propose another algorithm that combining SWFT and BM3D which improves the performance beyond BM3D.