Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance

Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial-spectral total variation (SSTV) regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell_1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regulariztion has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier (ALM) method. Finally, extensive experiments on simulated and real-world noise HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure

Non-local tensor completion for multitemporal remotely sensed images inpainting

Remotely sensed images may contain some missing areas because of poor weather conditions and sensor failure. Information of those areas may play an important role in the interpretation of multitemporal remotely sensed data. The paper aims at reconstructing the missing information by a non-local low-rank tensor completion method (NL-LRTC). First, nonlocal correlations in the spatial domain are taken into account by searching and grouping similar image patches in a large search window. Then low-rankness of the identified 4-order tensor groups is promoted to consider their correlations in spatial, spectral, and temporal domains, while reconstructing the underlying patterns. Experimental results on simulated and real data demonstrate that the proposed method is effective both qualitatively and quantitatively. In addition, the proposed method is computationally efficient compared to other patch based methods such as the recent proposed PM-MTGSR method

NEW ALGORITHMS FOR COMPRESSED SENSING OF MRI: WTWTS, DWTS, WDWTS

Magnetic resonance imaging (MRI) is one of the most accurate imaging techniques that can be used to detect several diseases, where other imaging methodologies fail. MRI data takes a longer time to capture. This is a pain taking process for the patients to remain still while the data is being captured. This is also hard for the doctor as well because if the images are not captured correctly then it will lead to wrong diagnoses of illness that might put the patients lives in danger. Since long scanning time is one of most serious drawback of the MRI modality, reducing acquisition time for MRI acquisition is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory is an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse signals while projection on a low dimensional linear subspace. Further enhancements have extended the CS framework by performing Variable Density Sampling (VDS) or using wavelet domain as sparsity basis generator. Recent work in this approach considers parent-child relations in the wavelet levels. This paper further extends the prior approach by utilizing the entire wavelet tree structure as an argument for coefficient correlation and also considers the directionality of wavelet coefficients using Hybrid Directional Wavelets (HDW). Incorporating coefficient thresholding in both wavelet tree structure as well as directional wavelet tree structure, the experiments reveal higher Signal to Noise ratio (SNR), Peak Signal to Noise ratio (PSNR) and lower Mean Square Error (MSE) for the CS based image reconstruction approach. Exploiting the sparsity of wavelet tree using the above-mentioned techniques achieves further lessening for data needed for the reconstruction, while improving the reconstruction result. These techniques are applied on a variety of images including both MRI and non-MRI data. The results show the efficacy of our techniques