The purpose of this paper is to investigate the feasibility of using a similarity coefficient map（SCM） in improving the morphological evaluation of T2＊ weighted（T2＊W） magnatic resonance imaging（MRI） for renal ...The purpose of this paper is to investigate the feasibility of using a similarity coefficient map（SCM） in improving the morphological evaluation of T2＊ weighted（T2＊W） magnatic resonance imaging（MRI） for renal cancer.Simulation studies and in vivo 12-echo T2＊W experiments for renal cancers were performed for this purpose.The results of the first simulation study suggest that an SCM can reveal small structures which are hard to distinguish from the background tissue in T2＊W images and the corresponding T2＊ map.The capability of improving the morphological evaluation is likely due to the improvement in the signal-to-noise ratio（SNR） and the carrier-to-noise ratio（CNR） by using the SCM technique.Compared with T2＊ W images,an SCM can improve the SNR by a factor ranging from 1.87 to 2.47.Compared with T2＊ maps,an SCM can improve the SNR by a factor ranging from 3.85 to 33.31.Compared with T2＊W images,an SCM can improve the CNR by a factor ranging from 2.09 to 2.43.Compared with T2＊ maps,an SCM can improve the CNR by a factor ranging from 1.94 to 8.14.For a given noise level,the improvements of the SNR and the CNR depend mainly on the original SNRs and CNRs in T2＊W images,respectively.In vivo experiments confirmed the results of the first simulation study.The results of the second simulation study suggest that more echoes are used to generate the SCM,and higher SNRs and CNRs can be achieved in SCMs.In conclusion,an SCM can provide improved morphological evaluation of T2＊W MR images for renal cancer by unveiling fine structures which are ambiguous or invisible in the corresponding T2＊W MR images and T2＊ maps.Furthermore,in practical applications,for a fixed total sampling time,one should increase the number of echoes as much as possible to achieve SCMs with better SNRs and CNRs.展开更多
Similarity coefficient mapping（SCM） aims to improve the morphological evaluation of T＊2weighted magnetic resonance imaging（T＊2-w MRI）. However, how to interpret the generated SCM map is still pending. Moreover, ...Similarity coefficient mapping（SCM） aims to improve the morphological evaluation of T＊2weighted magnetic resonance imaging（T＊2-w MRI）. However, how to interpret the generated SCM map is still pending. Moreover, is it probable to extract tissue dissimilarity messages based on the theory behind SCM？ The primary purpose of this paper is to address these two questions. First, the theory of SCM was interpreted from the perspective of linear fitting. Then, a term was embedded for tissue dissimilarity information. Finally, our method was validated with sixteen human brain image series from multiecho T＊2-w MRI. Generated maps were investigated from signal-to-noise ratio（SNR） and perceived visual quality, and then interpreted from intra- and inter-tissue intensity. Experimental results show that both perceptibility of anatomical structures and tissue contrast are improved. More importantly, tissue similarity or dissimilarity can be quantified and cross-validated from pixel intensity analysis. This method benefits image enhancement, tissue classification, malformation detection and morphological evaluation.展开更多
The generation of high-resolution DEM from interferometric SAR has resulted in the need for accurate and efficient methods of 2-dimensional phase unwrapping. In this paper, we give a brief description of the mathemati...The generation of high-resolution DEM from interferometric SAR has resulted in the need for accurate and efficient methods of 2-dimensional phase unwrapping. In this paper, we give a brief description of the mathematical base of phase unwrapping, and a detailed description of the unweighted and weighted least square phase unwrapping algorithm.Then our algorithm combining with the weighted least square phase unwrapping guided by the branch-cuts derived from Goldstein’ s algorithm and coherence coefficient map derived from the INSAR data is provided. In our experiment we write subroutines of the Goldstein’s branch-cut algorithm,unweighted and weighted least square phase unwrapping algorithm as well as our algorithm,and construct a small experiment system to resolve the phase unwrapping problem. Finally we test our algorithm on some INSAR data. The result shows that our approach can obtain unwrapped phase correctly and efficiently.展开更多
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo...Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.展开更多
Because man receives the vast amounts of information with visual sense, map representations and map manipulations are widely used in researching of various problems, and for the investigations of logic algebra. For bi...Because man receives the vast amounts of information with visual sense, map representations and map manipulations are widely used in researching of various problems, and for the investigations of logic algebra. For binary logic, the K-map, the b_j coefficient map and the R_j展开更多
Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate...Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher dimensions.These results generalize some known results.展开更多
Let S~* be the familiar class of normalized univalent functions in the unit disk.In [9], Keogh and Merkes proved that for a function f(z) = z +∑k=2∞ a_kz^k in the class S~*,then |a_3-λa_2~2| ≤ max{1, |3-4λ|}, λ...Let S~* be the familiar class of normalized univalent functions in the unit disk.In [9], Keogh and Merkes proved that for a function f(z) = z +∑k=2∞ a_kz^k in the class S~*,then |a_3-λa_2~2| ≤ max{1, |3-4λ|}, λ∈ C. In this article, we investigate the corresponding problem for the subclass of starlike mappings defined on the unit ball in a complex Banach space, on the unit polydisk in Cnand the bounded starlike circular domain in C~■, respectively.展开更多
基金Project supported by the National Basic Research Program of China (Grant No. 2011CB707701)the National Key Technology R&D Program of China(Grant Nos. 2011BAI12B05 and 2012BAI23B07)
文摘The purpose of this paper is to investigate the feasibility of using a similarity coefficient map（SCM） in improving the morphological evaluation of T2＊ weighted（T2＊W） magnatic resonance imaging（MRI） for renal cancer.Simulation studies and in vivo 12-echo T2＊W experiments for renal cancers were performed for this purpose.The results of the first simulation study suggest that an SCM can reveal small structures which are hard to distinguish from the background tissue in T2＊W images and the corresponding T2＊ map.The capability of improving the morphological evaluation is likely due to the improvement in the signal-to-noise ratio（SNR） and the carrier-to-noise ratio（CNR） by using the SCM technique.Compared with T2＊ W images,an SCM can improve the SNR by a factor ranging from 1.87 to 2.47.Compared with T2＊ maps,an SCM can improve the SNR by a factor ranging from 3.85 to 33.31.Compared with T2＊W images,an SCM can improve the CNR by a factor ranging from 2.09 to 2.43.Compared with T2＊ maps,an SCM can improve the CNR by a factor ranging from 1.94 to 8.14.For a given noise level,the improvements of the SNR and the CNR depend mainly on the original SNRs and CNRs in T2＊W images,respectively.In vivo experiments confirmed the results of the first simulation study.The results of the second simulation study suggest that more echoes are used to generate the SCM,and higher SNRs and CNRs can be achieved in SCMs.In conclusion,an SCM can provide improved morphological evaluation of T2＊W MR images for renal cancer by unveiling fine structures which are ambiguous or invisible in the corresponding T2＊W MR images and T2＊ maps.Furthermore,in practical applications,for a fixed total sampling time,one should increase the number of echoes as much as possible to achieve SCMs with better SNRs and CNRs.
基金Project supported in part by the National High Technology Research and Development Program of China(Grant Nos.2015AA043203 and 2012AA02A604)the National Natural Science Foundation of China(Grant Nos.81171402+8 种基金61471349and 81501463)the Innovative Research Team Program of Guangdong Province,China(Grant No.2011S013)the Science and Technological Program for Higher Education,Science and Researchand Health Care Institutions of Guangdong ProvinceChina(Grant No.2011108101001)the Natural Science Foundation of Guangdong Province,China(Grant No.2014A030310360)the Fundamental Research Program of Shenzhen City,China(Grant No.JCYJ20140417113430639)Beijing Center for Mathematics and Information Interdisciplinary Sciences,China
文摘Similarity coefficient mapping（SCM） aims to improve the morphological evaluation of T＊2weighted magnetic resonance imaging（T＊2-w MRI）. However, how to interpret the generated SCM map is still pending. Moreover, is it probable to extract tissue dissimilarity messages based on the theory behind SCM？ The primary purpose of this paper is to address these two questions. First, the theory of SCM was interpreted from the perspective of linear fitting. Then, a term was embedded for tissue dissimilarity information. Finally, our method was validated with sixteen human brain image series from multiecho T＊2-w MRI. Generated maps were investigated from signal-to-noise ratio（SNR） and perceived visual quality, and then interpreted from intra- and inter-tissue intensity. Experimental results show that both perceptibility of anatomical structures and tissue contrast are improved. More importantly, tissue similarity or dissimilarity can be quantified and cross-validated from pixel intensity analysis. This method benefits image enhancement, tissue classification, malformation detection and morphological evaluation.
基金Project supported by the National Natural Science Foundation of China(No.69782001)
文摘The generation of high-resolution DEM from interferometric SAR has resulted in the need for accurate and efficient methods of 2-dimensional phase unwrapping. In this paper, we give a brief description of the mathematical base of phase unwrapping, and a detailed description of the unweighted and weighted least square phase unwrapping algorithm.Then our algorithm combining with the weighted least square phase unwrapping guided by the branch-cuts derived from Goldstein’ s algorithm and coherence coefficient map derived from the INSAR data is provided. In our experiment we write subroutines of the Goldstein’s branch-cut algorithm,unweighted and weighted least square phase unwrapping algorithm as well as our algorithm,and construct a small experiment system to resolve the phase unwrapping problem. Finally we test our algorithm on some INSAR data. The result shows that our approach can obtain unwrapped phase correctly and efficiently.
基金Supported by the NNSF of China(11971165)the Natural Science Foundation of Zhejiang Province(LY21A010003)。
文摘Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.
文摘Because man receives the vast amounts of information with visual sense, map representations and map manipulations are widely used in researching of various problems, and for the investigations of logic algebra. For binary logic, the K-map, the b_j coefficient map and the R_j
基金National Natural Science Foundation of China(11971165,11561030)。
文摘Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher dimensions.These results generalize some known results.
基金This work was supported by NNSF of China（Grant Nos. 11561030, 11261022）, the Jiangxi Provincial Natural Science Foundation of China （Grant Nos. 20152ACB20002, 20161BAB201019）, Natural Science Foundation of Department of Education of Jiangxi Province, China （Grant No. GJJ150301）, and the Jiangxi Provincial graduate student innovation project （Grant No. YC2016-S159）
文摘Let S~* be the familiar class of normalized univalent functions in the unit disk.In [9], Keogh and Merkes proved that for a function f(z) = z +∑k=2∞ a_kz^k in the class S~*,then |a_3-λa_2~2| ≤ max{1, |3-4λ|}, λ∈ C. In this article, we investigate the corresponding problem for the subclass of starlike mappings defined on the unit ball in a complex Banach space, on the unit polydisk in Cnand the bounded starlike circular domain in C~■, respectively.
