Denoising of Rician corrupted 3D magnetic resonance images using tensor -SVD

Khaleel, Hawazin S.; Sagheer, Sameera V. Mohd; Baburaj, M; George, Sudhish N.

doi:10.1016/j.bspc.2018.04.004

Cited by 25 publications

(11 citation statements)

References 36 publications

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“…Shi et al (2015) proposed an MR image super-resolution method that integrated both local and global information for effective image recovery via total variation and low-rank tensor regularizations, respectively. A few LRTD-based image denoising methods were proposed for MR (Khaleel et al, 2018;Fu and Dong, 2016) and CT images (Sagheer and George, 2019) to reduce noise and artifacts introduced during image acquisition. Jiang et al (2020) proposed a functional connectivity network estimation approach by the assumption that the functional connectivity networks have similar topology across subjects via the LRTD.…”

Section: Low-rank Tensor Decomposition For Medical Image Computingmentioning

confidence: 99%

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Multi-Slice Low-Rank Tensor Decomposition Based Multi-Atlas Segmentation: Application to Automatic Pathological Liver CT Segmentation

Shi

Xian

Zhou

et al. 2021

Preprint

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Liver segmentation from abdominal CT images is an essential step for liver cancer computer-aided diagnosis and surgical planning. However, both the accuracy and robustness of existing liver segmentation methods cannot meet the requirements of clinical applications. In particular, for the common clinical cases where the liver tissue contains major pathology, current segmentation methods show poor performance. In this paper, we propose a novel low-rank tensor decomposition (LRTD) based multi-atlas segmentation (MAS) framework that achieves accurate and robust pathological liver segmentation of CT images. Firstly, we propose a multi-slice LRTD scheme to recover the underlying low-rank structure embedded in 3D medical images. It performs the LRTD on small image segments consisting of multiple consecutive image slices. Then, we present an LRTD-based atlas construction method to generate tumor-free liver atlases that mitigates the performance degradation of liver segmentation due to the presence of tumors. Finally, we introduce an LRTD-based MAS algorithm to derive patient-specific liver atlases for each test image, and to achieve accurate pairwise image registration and label propagation. Extensive experiments on three public databases of pathological liver cases validate the effectiveness of the proposed method. Both qualitative and quantitative results demonstrate that, in the presence of major pathology, the proposed method is more accurate and robust than state-of-the-art methods.

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Section: Low-rank Tensor Decomposition For Medical Image Computingmentioning

confidence: 99%

“…Then the tensor singular value thresholding (t-SVT) algorithm is used to recover the underlying low-rank structure. The general scheme is also applicable to other medical imaging modalities and organs ( Qin et al (2019); Xian et al (2018); Khaleel et al (2018)) (Section 4.1).…”

Section: Introductionmentioning

confidence: 99%

Multi-Slice Low-Rank Tensor Decomposition Based Multi-Atlas Segmentation: Application to Automatic Pathological Liver CT Segmentation

Shi

Xian

Zhou

et al. 2021

Preprint

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“…Recently, the tensor T-product has been established and proved to be a useful tool in many areas, such as image processing [28,29,42,47,50,60], computer vision [4,17,53,55], signal processing [10,34,37,48], low rank tensor recovery and robust tensor PCA [32,34], data completion and denoising [12,25,26,35,37,39,41,45,51,54,56,57,58,59]. Because of the importance of tensor T-product, Lund [38] gave the definition for tensor functions based on the T-product of third-order F-square tensors which means all the front slices of a tensor is square matrices.…”

Section: Introductionmentioning

confidence: 99%

Generalized tensor function via the tensor singular value decomposition based on the T-product

Miao

Wei

2020

Linear Algebra and its Applications

102

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In this paper, we present the definition of generalized tensor function according to the tensor singular value decomposition (T-SVD) based on the tensor T-product. Also, we introduce the compact singular value decomposition (T-CSVD) of tensors, from which the projection operators and Moore Penrose inverse of tensors are obtained. We establish the Cauchy integral formula for tensors by using the partial isometry tensors and applied it into the solution of tensor equations. Then we establish the generalized tensor power and the Taylor expansion of tensors. Explicit generalized tensor functions are listed. We define the tensor bilinear and sesquilinear forms and proposed theorems on structures preserved by generalized tensor functions. For complex tensors, we established an isomorphism between complex tensors and real tensors. In the last part of our paper, we find that the block circulant operator established an isomorphism between tensors and matrices. This isomorphism is used to prove the F-stochastic structure is invariant under generalized tensor functions. The concept of invariant tensor cones is raised.

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“…Among the many problems described by high-dimensional arrays (or tensors), third-order tensors have become increasingly prevalent in recent years with the emergence of the tensor T-product, which is a new type of multiplication between third-order tensors introduced by Kilmer, Martin, and Perrone [1]. The tensor T-product has shown to be a useful tool arising in a wide variety of application areas, including, but not limited to, image processing [2][3][4][5][6][7], computer vision [8][9][10][11][12], signal processing, low rank tensor recovery and robust tensor PCA [13][14][15][16][17][18], and data completion and denoising [19][20][21][22][23][24][25][26][27][28][29][30][31], because the tensor T-product provides an effective approach to transform the tensor multiplication into block diagonal matrix multiplication in the discrete Fourier domain.…”

Section: Introductionmentioning

confidence: 99%

“…, unf oldpX ´Ă X qy " xbcircp∇2 T f pU qq ¨unf oldpX ´Ă X q, unf oldpX ´Ă X qy " xunf oldp∇2 T f pU q ˚pX ´Ă X qq, unf oldpX ´Ă X qy " x∇ 2 T f p Ă X `tpX ´Ă X qq ˚pX ´Ă X q, X ´Ă X y.Thus, ϕ 1 p0q " x∇f p Ă X q, X ´Ă X y and ϕ 2 p0q " x∇ 2 T f p Ă X q ˚pX ´Ă X q, X ´Ă X y. It follows from the mean value theorem, that there exists some β P p0, 1q such that ϕp1q " ϕp0q `ϕ1 p0q `1 2 ϕ 2 pβq, which implies thatf pX q " f p Ă X q `x∇f p Ă X q, X ´Ă X y `1 2 x∇ 2 T f pZ q ˚pX ´Ă X q, X ´Ă X y,where Z " βX `p1 ´βq Ă X , i.e., the result in (i) holds.…”

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confidence: 99%

T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming

Zheng

Huang

Wang

2020

Preprint

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The T-product for third-order tensors has been used extensively in the literature. In this paper, we first introduce the first-order and second-order T-derivatives for the multi-vector real-valued function with the tensor T-product; and inspired by an equivalent characterization of a twice continuously T-differentiable multi-vector real-valued function being convex, we present a definition of the T-positive semidefiniteness of third-order symmetric tensors. After that, we extend many properties of positive semidefinite matrices to the case of third-order symmetric tensors. In particular, analogue to the widely used semidefinite programming (SDP for short), we introduce the semidefinite programming over the third-order symmetric tensor space (T-semidefinite programming or TSDP for short), and provide a way to solve the TSDP problem by converting it into an SDP problem in the complex domain. Furthermore, we give several examples which can be formulated (or relaxed) as TSDP problems, and report preliminary numerical results for two unconstrained polynomial optimization problems. Experiments show that finding the global minimums of polynomials via the TSDP relaxation outperforms the traditional SDP relaxation for the test examples.

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Denoising of Rician corrupted 3D magnetic resonance images using tensor -SVD

Cited by 25 publications

References 36 publications

Multi-Slice Low-Rank Tensor Decomposition Based Multi-Atlas Segmentation: Application to Automatic Pathological Liver CT Segmentation

Multi-Slice Low-Rank Tensor Decomposition Based Multi-Atlas Segmentation: Application to Automatic Pathological Liver CT Segmentation

Generalized tensor function via the tensor singular value decomposition based on the T-product

T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming

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