matlab毕业设计外文翻译--复杂脊波图像去噪(编辑修改稿)

matlab毕业设计外文翻译--复杂脊波图像去噪(编辑修改稿)内容摘要：

culties. We know that the ridgelet transform has been successfully used to analyze digital images. Unlike wavelet transforms, the ridgelet transform processes data by first puting integrals over different orientations and locations. A ridgelet is constant along the lines x1cos_ + x2sin_ = constant. In the direction orthogonal to these ridges it is a have been successfully applied in image denoising recently. In this paper, we bine the dualtree plex wavelet in the ridgelet transform and apply it to image denoising. The approximate shift invariance property of the dualtree plex wavelet and the good property of the ridgelet make our method a very good method for image results show that by using dualtree plex ridgelets, our algorithms obtain higher Peak Signal to Noise Ratio (PSNR) for all the denoised images with di_erent noise organization of this paper is as follows. In Section 2, we explain how to incorporate the dualtree plex wavelets into the ridgelet transform for image denoising. Experimental results are conducted in Section 3. Finally we give the conclusion and future work to be done in section 4. 2 Image Denoising by using Complex Ridgelets Discrete ridgelet transform provides nearideal sparsity of representation of both smooth objects and of objects with edges. It is a nearoptimal method of denoising for Gaussian noise. The ridgelet transform can press the energy of the image into a smaller number of ridgelet coe_cients. On the other hand, the wavelet transform produces many large wavelet coe_cients on the edges on every scale of the 2D wavelet deposition. This means that many wavelet coe_cients are needed in order to reconstruct the edges in the image. We know that approximate Radon transforms for digital data can be based on discrete fast Fouriertransform. The ordinary ridgelet transform can be achieved as follows: 1. Compute the 2D FFT of the image. 2. Substitute the sampled values of the Fourier transform obtained on the square lattice with sampled values on a polar lattice. 3. Compute the 1D inverse FFT on each angular line. 4. Perform the 1D scalar wavelet transform on the resulting angular lines in order to obtain the ridgelet coe_cients. It is well known that the ordinary discrete wavelet transform is not shift invariant because of the decimation operation during the transform. A small shift in the input signal can cause very di_erent output wavelet coe_cients. In order to overe this problem, Kingsbury introduced a new kind of wavelet transform, called the dualtree plex wavelet transform, that exhibits approximate shift invariant property and improved angular resolution. Since the scalar wavelet is not shift invariant, it is better to apply the dualtree plex wavelet in the ridgelet transform so that we can have what we call plex ridgelets. This can be done by replacing the 1D scalar wavelet with the 1D dualtree plex wavelet transform in the last step of the ridgelet transform. In this way, we can bine the good property of the ridgelet transform with the approximate shift invariant property of the dualtree plex wavelets. The plex ridgelet transform can be applied to the entire image or we can partition the image into a number of overlapping squares and we apply。