SAR image de-noising based on texture strength and weighted nuclear norm minimization

As synthetic aperture radar（SAR） has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization（WNNM） is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis（PCA） and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures（BLS-GSM） method, non-local means（NLM） filtering in terms of both quantitative measure and visual perception quality.

IMPULSE NOISE REMOVAL BY L1 WEIGHTED NUCLEAR NORM MINIMIZATION

In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.

STABLE AND ROBUST RECOVERY OF APPROXIMATELY k-SPARSE SIGNALS WITH PARTIAL SUPPORT INFORMATION IN NOISE SETTINGS VIA WEIGHTED ℓ_(p)(0

In the existing work,the recovery of strictly k-sparse signals with partial support information was derived in theℓ2 bounded noise setting.In this paper,the recovery of approximately k-sparse signals with partial support information in two noise settings is investigated via weightedℓp(0<p≤1)minimization method.The restricted isometry constant(RIC)conditionδt k<1 pη2 p−1+1 on the measurement matrix for some t∈[1+2−p 2+pσ,2]is proved to be sufficient to guarantee the stable and robust recovery of signals under sparsity defect in noisy cases.Herein,σ∈[0,1]is a parameter related to the prior support information of the original signal,andη≥0 is determined by p,t andσ.The new results not only improve the recent work in[17],but also include the optimal results by weightedℓ1 minimization or by standardℓp minimization as special cases.

De-noising research on terahertz holographic reconstructed image based on weighted nuclear norm minimization method

Terahertz imaging is one of the forefront topics of imaging technology today. Denoising process is the key for improving the resolution of the terahertz holographic reconstructed image. Based on the fact that the weighted nuclear norm minimization （WNNM） method preserves the details of the reconstructed image well and the non- local mean （NLM） algorithm performs better in the removal of background noise, this paper proposes a new method in which the NLM algorithm is used to improve the WNNM method. The experimental observation and quantitative analysis of the denoising results prove that the new method has better denoising effect for the terahertz holographic reconstructed image.

Weighted ■_(p)-Minimization for Sparse Signal Recovery under Arbitrary Support Prior

Weighted ■_(p)(0<p<l)minimization has been extensively studied as an effective way to reconstruct a sparse signal from compressively sampled measurements when some prior support information of the signal is available.In this paper,we consider the recovery guarantees of Κ-sparse signals via the weighted ■_(p)(0<P<1)minimization when arbitrarily many support priors are given.Our analysis enables an extension to existing works that assume only a single support prior is used.

EQUIVALENCE BETWEEN NONNEGATIVE SOLUTIONS TO PARTIAL SPARSE AND WEIGHTED l_1-NORM MINIMIZATIONS

Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.

l_(1)-norm Based GWLP for Robust Frequency Estimation

In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.

A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images

Ultrasound is a low-cost,non-invasive and real-time imaging modality that has proved popular for many medical applications.Unfortunately,the acquired ultrasound images are often corrupted by speckle noise from scatterers smaller than ultrasound beam wavelength.The signal-dependent speckle noise makes visual observation difficult.In this paper,we propose a patch-based low-rank approach for reducing the speckle noise in ultrasound images.After constructing the patch group of the ultrasound images by the block-matching scheme,we establish a variational model using the weighted nuclear norm as a regularizer for the patch group.The alternating direction method of multipliers(ADMM)is applied for solving the established nonconvex model.We return all the approximate patches to their original locations and get the final restored ultrasound images.Experimental results are given to demonstrate that the proposed method outperforms some existing state-of-the-art methods in terms of visual quality and quantitative measures.

Improved image denoising via RAISR with fewer filters

In recent years,accurate Gaussian noise removal has attracted considerable attention for mobile applications,as in smart phones.Accurate conventional denoising methods have the potential ability to improve denoising performance with no additional time.Therefore,we propose a rapid post-processing method for Gaussian noise removal in this paper.Block matching and 3D filtering and weighted nuclear norm minimization are utilized to suppress noise.Although these nonlocal image denoising methods have quantitatively high performance,some fine image details are lacking due to the loss of high frequency information.To tackle this problem,an improvement to the pioneering RAISR approach(rapid and accurate image super-resolution),is applied to rapidly post-process the denoised image.It gives performance comparable to state-of-the-art super-resolution techniques at low computational cost,preserving important image structures well.Our modification is to reduce the hash classes for the patches extracted from the denoised image and the pixels from the ground truth to 18 filters by two improvements:geometric conversion and reduction of the strength classes.In addition,following RAISR,the census transform is exploited by blending the image processed by noise removal methods with the filtered one to achieve artifact-free results.Experimental results demonstrate that higher quality and more pleasant visual results can be achieved than by other methods,efficiently and with low memory requirements.