The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Color-decoupled photo response non-uniformity for digital image forensics

The last few years have seen the use of photo response non-uniformity noise (PRNU), a unique fingerprint of imaging sensors, in various digital forensic applications such as source device identification, content integrity verification and authentication. However, the use of a colour filter array for capturing only one of the three colour components per pixel introduces colour interpolation noise, while the existing methods for extracting PRNU provide no effective means for addressing this issue. Because the artificial colours obtained through the colour interpolation process is not directly acquired from the scene by physical hardware, we expect that the PRNU extracted from the physical components, which are free from interpolation noise, should be more reliable than that from the artificial channels, which carry interpolation noise. Based on this assumption we propose a Couple-Decoupled PRNU (CD-PRNU) extraction method, which first decomposes each colour channel into 4 sub-images and then extracts the PRNU noise from each sub-image. The PRNU noise patterns of the sub-images are then assembled to get the CD-PRNU. This new method can prevent the interpolation noise from propagating into the physical components, thus improving the accuracy of device identification and image content integrity verification

Wavelet-Based Enhancement Technique for Visibility Improvement of Digital Images

Image enhancement techniques for visibility improvement of color digital images based on wavelet transform domain are investigated in this dissertation research. In this research, a novel, fast and robust wavelet-based dynamic range compression and local contrast enhancement (WDRC) algorithm to improve the visibility of digital images captured under non-uniform lighting conditions has been developed. A wavelet transform is mainly used for dimensionality reduction such that a dynamic range compression with local contrast enhancement algorithm is applied only to the approximation coefficients which are obtained by low-pass filtering and down-sampling the original intensity image. The normalized approximation coefficients are transformed using a hyperbolic sine curve and the contrast enhancement is realized by tuning the magnitude of the each coefficient with respect to surrounding coefficients. The transformed coefficients are then de-normalized to their original range. The detail coefficients are also modified to prevent edge deformation. The inverse wavelet transform is carried out resulting in a lower dynamic range and contrast enhanced intensity image. A color restoration process based on the relationship between spectral bands and the luminance of the original image is applied to convert the enhanced intensity image back to a color image. Although the colors of the enhanced images produced by the proposed algorithm are consistent with the colors of the original image, the proposed algorithm fails to produce color constant results for some pathological scenes that have very strong spectral characteristics in a single band. The linear color restoration process is the main reason for this drawback. Hence, a different approach is required for tackling the color constancy problem. The illuminant is modeled having an effect on the image histogram as a linear shift and adjust the image histogram to discount the illuminant. The WDRC algorithm is then applied with a slight modification, i.e. instead of using a linear color restoration, a non-linear color restoration process employing the spectral context relationships of the original image is applied. The proposed technique solves the color constancy issue and the overall enhancement algorithm provides attractive results improving visibility even for scenes with near-zero visibility conditions. In this research, a new wavelet-based image interpolation technique that can be used for improving the visibility of tiny features in an image is presented. In wavelet domain interpolation techniques, the input image is usually treated as the low-pass filtered subbands of an unknown wavelet-transformed high-resolution (HR) image, and then the unknown high-resolution image is produced by estimating the wavelet coefficients of the high-pass filtered subbands. The same approach is used to obtain an initial estimate of the high-resolution image by zero filling the high-pass filtered subbands. Detail coefficients are estimated via feeding this initial estimate to an undecimated wavelet transform (UWT). Taking an inverse transform after replacing the approximation coefficients of the UWT with initially estimated HR image, results in the final interpolated image. Experimental results of the proposed algorithms proved their superiority over the state-of-the-art enhancement and interpolation techniques

Image up-sampling using the discrete wavelet transform

Image up-sampling is an effective technique, useful in today\u27s digital image processing applications and rendering devices. In image up-sampling, an image is enhanced from a lower resolution to a higher resolution with the degree of enhancement depending upon application requirements. It is known that the traditional interpolation based approaches for up-sampling, such as the Bilinear or Bicubic interpolations, blur the resultant images along edges and image features. Furthermore, in color imagery, these interpolation-based up-sampling methods may have color infringing artifacts in the areas where the images contain sharp edges and fine textures. We present an interesting up-sampling algorithm based on the Discrete Wavelet Transform (DWT). The proposed method preserves much of the sharp edge features in the image, and lessens the amount of color artifacts. Effectiveness of the proposed algorithm has been demonstrated based on comparison of PSNR and Δ E * ab quality metrics between the original and reconstructed images