SURE-LET Approach Research Articles

Improved Interscale-Based SURE-LET Approach to Image Denoising

Currently, the SURE-LET approach has been widely used for the removal of noise in corrupted image. However the original interscale-based SURE-LET approach rules out intrascale considerations of wavelet coefficients, which makes the denoising ability of the technique is reduced greatly. In this paper, the local Wiener-like estimator is incorporated into the original interscale-based SURE-LET thresholding function. The tests show the improved interscale-based SURE-LET gets the better denoising performance objectively and subjectively. Especially for Barbara image, the PSNR is on average improved by 0.52dB compared to the traditional pointwise interscale-based SURE-LET approach.

An Extension of the Interscale SURE-LET Approach for Image Denoising

In this paper, an extension of the interscale SURE-LET approach exploiting the interscale and intrascale dependencies of wavelet coefficients is proposed to improve denoising performance. This method incorporates information on neighbouring coefficients into the linear expansion of thresholds (LETs) without additional parameters to capture the texture characteristics of this image. The resulting interscale-intrascale wavelet estimator consists of a linear expansion of multivariate thresholding functions, whose parameters are optimized thanks to a multivariate Stein's unbiased risk estimate (SURE). Some experimental results are given to demonstrate the strength of the proposed method.

Multi-Wiener SURE-LET Deconvolution

In this paper, we propose a novel deconvolution algorithm based on the minimization of a regularized Stein's unbiased risk estimate (SURE), which is a good estimate of the mean squared error. We linearly parametrize the deconvolution process by using multiple Wiener filters as elementary functions, followed by undecimated Haar-wavelet thresholding. Due to the quadratic nature of SURE and the linear parametrization, the deconvolution problem finally boils down to solving a linear system of equations, which is very fast and exact. The linear coefficients, i.e., the solution of the linear system of equations, constitute the best approximation of the optimal processing on the Wiener-Haar-threshold basis that we consider. In addition, the proposed multi-Wiener SURE-LET approach is applicable for both periodic and symmetric boundary conditions, and can thus be used in various practical scenarios. The very competitive (both in computation time and quality) results show that the proposed algorithm, which can be interpreted as a kind of nonlinear Wiener processing, can be used as a basic tool for building more sophisticated deconvolution algorithms.

The SURE-LET Approach for MR Brain Image Denoising Using Different Shrinkage Rules

SURE-LET Approach is used for reducing or removing noise in brain Magnetic Resonance Images (MRI). Removing or reducing noise is an active research area in image processing. Rician noise is the dominant noise in MRIs. Due to this type of noise, the abnormal tissue (cancerous tissue) may be misclassified as normal tissue and introduces bias into MRI measurements that can have signi?cant impact on the shapes and orientations of tensors in di?usion tensor MRIs. SURE is a new approach to Orthonormal wavelet image denoising. It is an image-domain minimization of an estimate of the mean squared error—Stein’s unbiased risk estimates (SURE). Here, the denoising process can be expressed as a linear combination of elementary denoising processes-linear expansion of thresholds (LET). Different Shrinkage functions such as Soft and Hard and Shrinkage rules and Universal and BayesShrink are used to remove noise and the performance of these results are compared. The algorithm is applied on brain MRIs with different noisy conditions by varying standard deviation of noise. The performance of this approach is compared with performance of the Curvelet transform.

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algorithm is parameterized as a linear expansion of thresholds (LET) and optimized using Stein's unbiased risk estimate (SURE). The proposed wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels, as well as on their parents in the coarser wavelet subband. A nonredundant, orthonormal, wavelet transform is first applied to the noisy data, followed by the (subband-dependent) vector-valued thresholding of individual multichannel wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform. Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that despite being nonredundant, our algorithm matches the quality of the best redundant approaches, while maintaining a high computational efficiency and a low CPU/memory consumption. An online Java demo illustrates these assertions.

The SURE-LET Approach to Image Denoising

We propose a new approach to image denoising, based on the image-domain minimization of an estimate of the mean squared error--Stein's unbiased risk estimate (SURE). Unlike most existing denoising algorithms, using the SURE makes it needless to hypothesize a statistical model for the noiseless image. A key point of our approach is that, although the (nonlinear) processing is performed in a transformed domain--typically, an undecimated discrete wavelet transform, but we also address nonorthonormal transforms--this minimization is performed in the image domain. Indeed, we demonstrate that, when the transform is a "tight" frame (an undecimated wavelet transform using orthonormal filters), separate subband minimization yields substantially worse results. In order for our approach to be viable, we add another principle, that the denoising process can be expressed as a linear combination of elementary denoising processes--linear expansion of thresholds (LET). Armed with the SURE and LET principles, we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient. Quite remarkably, the very competitive results obtained by performing a simple threshold (image-domain SURE optimized) on the undecimated Haar wavelet coefficients show that the SURE-LET principle has a huge potential.