scholarly journals Non-Local SVD Denoising of MRI Based on Sparse Representations

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1536 ◽  
Author(s):  
Nallig Leal ◽  
Eduardo Zurek ◽  
Esmeide Leal
Keyword(s):  
Sparse Representation ◽  
Diagnostic Errors ◽  
Diagnostic Technique ◽  
Real Data ◽  
Sparse Representations ◽  
Local Approach ◽  
Residual Noise ◽  
Non Local ◽  
Value Decomposition ◽  
Global Influence

Magnetic Resonance (MR) Imaging is a diagnostic technique that produces noisy images, which must be filtered before processing to prevent diagnostic errors. However, filtering the noise while keeping fine details is a difficult task. This paper presents a method, based on sparse representations and singular value decomposition (SVD), for non-locally denoising MR images. The proposed method prevents blurring, artifacts, and residual noise. Our method is composed of three stages. The first stage divides the image into sub-volumes, to obtain its sparse representation, by using the KSVD algorithm. Then, the global influence of the dictionary atoms is computed to upgrade the dictionary and obtain a better reconstruction of the sub-volumes. In the second stage, based on the sparse representation, the noise-free sub-volume is estimated using a non-local approach and SVD. The noise-free voxel is reconstructed by aggregating the overlapped voxels according to the rarity of the sub-volumes it belongs, which is computed from the global influence of the atoms. The third stage repeats the process using a different sub-volume size for producing a new filtered image, which is averaged with the previously filtered images. The results provided show that our method outperforms several state-of-the-art methods in both simulated and real data.

scholarly journals Fusion of Hyperspectral and Multispectral Images Based on a Centralized Non-local Sparsity Model of Abundance Maps

Tecnura ◽  
2020 ◽  
Vol 24 (66) ◽  
pp. 62-75
Author(s):  
Edwin Vargas ◽  
Kevin Arias ◽  
Fernando Rojas ◽  
Henry Arguello
Keyword(s):  
Image Fusion ◽  
Sparse Representation ◽  
Spatial Resolution ◽  
Real Data ◽  
Spectral Unmixing ◽  
Multispectral Images ◽  
Self Similarity ◽  
Diverse Range ◽  
Learned Dictionary ◽  
Non Local

Objective: Hyperspectral (HS) imaging systems are commonly used in a diverse range of applications that involve detection and classification tasks. However, the low spatial resolution of hyperspectral images may limit the performance of the involved tasks in such applications. In the last years, fusing the information of an HS image with high spatial resolution multispectral (MS) or panchromatic (PAN) images has been widely studied to enhance the spatial resolution. Image fusion has been formulated as an inverse problem whose solution is an HS image which assumed to be sparse in an analytic or learned dictionary. This work proposes a non-local centralized sparse representation model on a set of learned dictionaries in order to regularize the conventional fusion problem.Methodology: The dictionaries are learned from the estimated abundance data taking advantage of the depth correlation between abundance maps and the non-local self- similarity over the spatial domain. Then, conditionally on these dictionaries, the fusion problem is solved by an alternating iterative numerical algorithm.Results: Experimental results with real data show that the proposed method outperforms the state-of-the-art methods under different quantitative assessments.Conclusions: In this work, we propose a hyperspectral and multispectral image fusion method based on a non-local centralized sparse representation on abundance maps. This model allows us to include the non-local redundancy of abundance maps in the fusion problem using spectral unmixing and improve the performance of the sparsity-based fusion approaches.

Study on Over-Complete Dictionaries for Sparse Representations of Signals

2012 ◽  
Vol 157-158 ◽  
pp. 796-799
Author(s):  
Guang Chun Gao ◽  
Kai Xiong ◽  
Li Na Shang ◽  
Sheng Ying Zhao ◽  
Cui Zhang
Keyword(s):  
Inverse Problems ◽  
Compressed Sensing ◽  
Sparse Representation ◽  
Sparse Representations ◽  
Experimental Results ◽  
Decomposition Algorithm ◽  
Linear Combinations ◽  
Design Algorithm ◽  
Sparse Decomposition

In recent years there has been a growing interest in the study of sparse representation of signals. The redundancy of over-complete dictionary can make it effectively capture the characteristics of the signals. Using an over-complete dictionary that contains prototype signal-atoms, signals are described as linear combinations of a few of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, Compressed Sensing (CS), and more. Recent activities in this field concentrate mainly on the study of sparse decomposition algorithm and dictionary design algorithm. In this paper, we discuss the advantages of sparse dictionaries, and present the implicit dictionaries for signal sparse presents. The overcomplete dictionaries which combined the different orthonormal transform bases can be used for the compressed sensing. Experimental results demonstrate the effectivity for sparse presents of signals.

Fractional calculus in solid mechanics: local versus non-local approach

2009 ◽  
Vol T136 ◽  
pp. 014003 ◽  
Author(s):  
Alberto Carpinteri ◽  
Pietro Cornetti ◽  
Alberto Sapora ◽  
Mario Di Paola ◽  
Massimiliano Zingales
Keyword(s):  
Fractional Calculus ◽  
Solid Mechanics ◽  
Local Approach ◽  
Non Local

scholarly journals Deterministic Imputation in Multienvironment Trials

ISRN Agronomy ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Sergio Arciniegas-Alarcón ◽  
Marisol García-Peña ◽  
Wojtek Janusz Krzanowski ◽  
Carlos Tadeu dos Santos Dias
Keyword(s):  
Missing Values ◽  
Interaction Model ◽  
Environmental Parameters ◽  
Real Data ◽  
Original Data ◽  
Genotype By Environment Interaction ◽  
Environment Interaction ◽  
Data Set ◽  
Value Decomposition ◽  
Main Effects

This paper proposes five new imputation methods for unbalanced experiments with genotype by-environment interaction (G×E). The methods use cross-validation by eigenvector, based on an iterative scheme with the singular value decomposition (SVD) of a matrix. To test the methods, we performed a simulation study using three complete matrices of real data, obtained from G×E interaction trials of peas, cotton, and beans, and introducing lack of balance by randomly deleting in turn 10%, 20%, and 40% of the values in each matrix. The quality of the imputations was evaluated with the additive main effects and multiplicative interaction model (AMMI), using the root mean squared predictive difference (RMSPD) between the genotypes and environmental parameters of the original data set and the set completed by imputation. The proposed methodology does not make any distributional or structural assumptions and does not have any restrictions regarding the pattern or mechanism of missing values.

Sign in / Sign up

Export Citation Format

Share Document