Medical Image Fusion Based on Joint Sparse Method

Medical Image Fusion Based on Joint Sparse Method I. INTRODUCTION From the identical scene number of images can be obtained concurrently by utilizing dissimilar sensors. Using the many sensors to identify the picture complete of scene from the obtained images is highly impossible. For this here using image fusion algorithm it will accept the mixing of multiple obtained images to produce number of useful complex image integrating the opposite information from the many sensors, yet, they are out of boundary and of dissimilar declaration. In medical diagnosis we will find the medical imaging. After completing the diagnosis the imaging movements are like magnetic resonance imaging (MRI) and computed tomography (CT) it will gives dissimilar view in the same scene, which can be delay clinical decision making and the diagnostic process. For example MRI gives the perspectives of soft materials, while CT for bone structures evaluation. For accurate diagnosis this inspires the necessary for image fusion by combining the reciprocal information. Three problems to be notified while fusing the images [1] are: 1) the fused image should preserve all the important information needed for further processing. 2) Artifacts should not be introduced in fused image. 3) Noise and unimportant information should be suppressed. Several dissimilar Greedy approaches using the sparse representation of the signal this signal is presently possible [3], Sparse representation of signals is now possible utilizing many different Greedy approaches [3], including: 1. Matching Pursuit (MP) [3] 2. Orthogonal Matching Pursuit (OMP) [3], and 3.Stage wise Orthogonal Matching Pursuit (St OMP) [4]. These techniques are used to represent signals with the fewest number of non-zero coefficients. Principal Component Analysis (PCA) [5] is one of the powerful state-of-the-art image fusion approaches in terms of visual inspection and quantitative evaluation metrics. This fusion is carried out by integrating the principal components of images to be fused. Both PCA and Sparse fusion have specific advantages and disadvantages. PCA fusion will enhance the spatial quality but have dense nonzero entries that might represent uninformative features. Sparse fusion preserves important information but high spatial resolution is lacking. This paper proposes a new algorithm inspired by [6], which employs different fusion rules for common and innovative sparse comp onents of the source images. The proposed algorithm utilizes the advantages of both PCA and Sparse representation for fusing common and innovative features of the captured images. This algorithm also overcomes the disadvantages of both PCA and Sparse representation. In this paper, we demonstrate the effectiveness of our proposed method by comparing its results with PCA and Sparse Fusion. II. SYSTEM DESIGN As discussed in the previous section, sparsest approximation is achieved through Greedy methods. In this section, we briefly explore the Orthogonal Matching Pursuit algorithm to achieve sparsest representation. These sparse coding algorithms are constructed based on the premise that Dictionary D of size nÃâ€"k is already known. For effective results, we use phase included DCT (Discrete Cosine Transform) dictionary [7] for our experiment. In this paper, we have customized OMP sparse coding algorithm for fusion purposes. The ultimate aim of OMP algorithm is to achieve best approximation. The mathematical formula for solving this constraint problem is given by: (1) (2) Where N is the number of non-zero coefficients. Equation 2 represents the definition for solving error constrained problem. Next atom to be added in this iterative framework is the atom which has highest correlation to the residual at each stage. Iteration is performed until it meets the stopping criterion. OMP is due to orthogonalization between atoms in the dictionary D and residual r. Pseudo Algorithm of OMP Given: Dictionary D, signal S, and error threshold à Ã‚ µ Initialize residual r0=S-Ds0, index set I0={} and main iteration is k = k+1 (initial k=0). Using the ideal solution à °Ã‚ Ã¢â‚¬ËœÃ‚ §Ãƒ °Ã‚ Ã¢â‚¬Ëœ- = à °Ã‚ Ã¢â‚¬ËœÃ¢â‚¬ËœÃƒ °Ã‚ Ã¢â‚¬Ëœ-à °Ã‚ Ã¢â‚¬ËœÃ¢â‚¬ ¡Ãƒ °Ã‚ Ã¢â‚¬ËœÃ… ¸Ãƒ °Ã‚ Ã¢â‚¬ËœÃ‹Å"−1/, Calculate the error (à °Ã‚ Ã¢â‚¬Ëœ-) = for all i. Update stage: Augmenting the index set à °Ã‚ Ã‚ Ã‚ ¼Ãƒ °Ã‚ Ã¢â‚¬ËœÃ‹Å" = à °Ã‚ Ã‚ Ã‚ ¼Ãƒ °Ã‚ Ã¢â‚¬ËœÃ‹Å"−1 ∠ª {à °Ã‚ Ã¢â‚¬Ëœ-0} (find i0 of (à °Ã‚ Ã¢â‚¬Ëœ-): ∀1 ≠¤ à °Ã‚ Ã¢â‚¬Ëœ- ≠¤ à °Ã‚ Ã¢â‚¬ËœÃ… ¡ and (à °Ã‚ Ã¢â‚¬Ëœ-0) ≠¤ (à °Ã‚ Ã¢â‚¬Ëœ-). Update the solution (à °Ã‚ Ã¢â‚¬Ëœ-0)+= à °Ã‚ Ã¢â‚¬ËœÃ‚ §Ãƒ °Ã‚ Ã¢â‚¬Ëœ- and residual. If stopping criterion is met, à °Ã‚ Ã¢â‚¬ËœÃ‚   = à °Ã‚ Ã¢â‚¬ËœÃ‚  Ãƒ °Ã‚ Ã¢â‚¬ËœÃ‹Å"; else, apply another iteration. III. PROPOSED SCHEME This work proposes a fusion method that employs PCA transformation and sparse transformation. An attempt is made to efficiently utilize the advantages of PCA and Sparse fusion scheme. The proposed fusion framework has been illustrated in Fig.1. Firstly, the common and innovative components are extracted from geometrically aligned multiple images of the same scene. Secondly, different fusion rules are adopted to fuse these coefficients. The algorithm is summarized as follows: 1) Registered multiple images in an ensemble have one common component and multiple innovative components. Innovative components contain the complementary information from different images of same scene 2) Innovative components of different images i are decomposed into sparse vectors s1,s2,s3,†¦si via orthogonal matching pursuit method described in Figure.1. Fig.1. Flow of Sparse PCA joint fusion algorithm 3) Combine the sparse coefficients of innovative components using PCA fusion rule, for which the covariance matrix s C of innovative images is calculated as follows, (3) Where s1,s2 are the sparse vectors of the innovative components. Find the Eigen sparse and normalized Eigen sparse vector of maximum Eigen value. Eigen vector will be used as weightings for innovative sparse vectors to be fused. 4) Fused PCA result Ip is reshaped into a block of 8Ãâ€"8 and each pixel position is the sum of several block values. Reconstructed image is obtained by dividing each pixel by number of addition operations performed at each pixel. 5) For fusing common component and fused innovative component, the fuse rule of weighted average scheme proposed by Burt et al. [2] is adopted. IV. EXPERIMENTAL RESULTS In order to test the performance of the proposed joint fusion algorithm, we compared the quantitative and qualitative results with two state the of art methods. Qualitative measurement is done through visual inspection that considers sharpness and noise suppression. Since the proposed joint fusion uses both PCA and sparse domain, we use PCA, Sparse OMP fusion methods for comparison. For the evaluation, we adopted proposed joint strategy for Multi resolution, Multi focus and Multimode images and compared the results with existing algorithms. Our experiment is carried out with the assumption that the source images are registered already. Fig. 2, shows results of fusion for the case of multi focus images. Based on visual inspection, The Joint PCA Sparse algorithm performs the best since the resultant image contain more geometric structures while sparse fusion comes the second. Result of proposed method seems to contain sharp edges. Fig.3, illustrates results of fusion of mutli dosage image results based on three different fusion algorithms. Low dose image seems to suffer from patchiness. As it can be observed, visually, Joint Sparse result shows the details clearly than the Low dose image. Visually, joint fusion resultant seems to be better than other 2 methods. Increasing the dosage might reduce the noise but harm patients. Low dose images are prone to noise. Fusing low dose and medium dose image should suppress the noise and enhance the informative details for precise diagnosis. Fig.4, illustrates the results of applying two multi modal medical images to three image fusion algorithms. The medical images are MRI and CT image of same scene which have been registered already. CT image provides the information on bone structures and MRI image contains tissue information. Medical image fusion needs great accuracy as it’s used for diagnosis. Hence, multimodal image fusion would give sufficient details necessary for diagnosis. Based on the visual inspection, the Joint Sparse results contain more detail information. Results of PCA seem to have high spatial resolution but they are disappointing in terms of detailed information. Bone details are not visible in PCA resultant image. Sparse result is better but some artifacts are easily observed Reconstructing fused image through joint fusion algorithms seems to be more precise comparatively. In order to analyze the quality of the algorithms quantitatively, we consider 5 metrics: Mutual Information (MI), PSNR, Correlation, Entropy and Structural Similarity (SSIM) index. Mutual Information shows how much information has been transferred from source images to the resultant images. Entropy shows the amount of important details available in the image. PSNR is Peak Signal to Noise Ration which is used to measure the reconstruction quality of fused image. PSNR of the fused image If is calculated using the standard formula: (4) Where M is the maximum possible pixel value of the image and MSE is the Mean Square error. The SSIM [8] provides structural information of objects and measures the similarity between the two images. Experiment results are shown in Table.1. Tabulated result demonstrates the effectiveness of the proposed algorithm over existing methods in terms of Qualitative and Quantitative methodologies. We can observe that the results of multimodal image fusion and multi focus image fusion utilizing our proposed fusion strategy outperforms PCA and Sparse fusion. The PCA by itself performs poorer results for all cases. Table 1 Performance Of Fusion Methods By The Quality Evaluation Metrics Image Type Fusion Stratergy PSNR(db) Mutual Information Entropy Correlation SSIM Multi focus Joint PCA Sparse 34.1742 2.1733 7.3656 0.9990 1.000 PCA 31.6321 2.0177 7.2607 0.9981 0.9999 OMP fusion 32.3392 2.0606 7.3654 0.9981 1.000 Multi dose Joint PCA Sparse 25.2115 0.7887 4.8643 0.9997 1 PCA 22.6994 0.7638 4.7905 0.9991 0.9997 OMP fusion 24.4680 0.7794 4.7937 0.9995 0.9998 Multimodal(MRICT) Joint PCA Sparse 26.4111 0.9634 6.7409 0.9403 .9977 PCA 20.8380 0.8096 6.5502 0.8690 .9919 OMP fusion 24.8056 0.9940 6.7376 0.8985 .9975 V. CONCLUSION Medical Image fusion plays an important role in clinical diagnosis. In this paper, a joint fusion modal is proposed based on sparse representation theory and PCA for multimodal and multi dose medical images. Visually and quantitatively, the experimental results show that the proposed method has effectively expressed the geometric structures and edges and has proved to perform better than PCA and OMP fusion. This modal can also be extended to fuse multiple source images from multi resolution, multiple spectral frequencies and multiple modalities. REFERENCES [1] S.G. Nikolov., P.R. Hill., D.R. Bull., C.N. Canagarajah.Wavelets for image fusion, A. Petrosian, F. Meyer (Eds.), Wavelets in Signal and Image Analysis, Computational Imaging and Vision Series, Kluwer Academic Publishers, Dordrecht, The Netherlands (2001). pp. 213–244. [2]P. Burt, R. Kolczynski, Enhanced image capture through fusion, Proceedings of the 4th International Conference on Computer Vision, 1993, pp. 173-182. [3] L. Rebolloà ¢Ã¢â€š ¬Ã‚ Neira and D. Lowe, Optimized orthogonal matching pursuit approach, IEEE Signal Processing Letters, pp.137–140, 2002. [4] D. Donoho and Y. Tsaig, Sparse solutions of underdetermined linear equations by stagewise orthogonal matching pursuit, Stanford University, Tech. report 2006. [5] M. R.Metwalli, A. H. Nasr, O. S. Farag Allah, and S. El-Rabaie†Image fusion based on Principal Component Analysis and High-pass Filter†, Proceedings of the IEEE/ ICCES 2009 international Conference, DEC. 14-16, 2009, pp. 63-70. [6] H. Yin, S. Li,†Multimodal image fusion with joint sparsity model†, Opt Eng., 50(6), (2011). [7] Z. Sadeghipour, M. Babaie-Zadeh, and C. Jutten, An adaptive thresholding approach for image denoising using redundant representations, IEEE international workshop on Machine Learning for Signal Processing, 2009, pp. 1-6. [8] Zhou Wang, Alan C. Bovik, Hamid R. Sheikh and Eero P. Simoncelli, â€Å"Image Quality Assessment: From Error Visibility to Structural Similarity†, IEEE transactions on Image Processing, vol. 13, no. 4, April 2004.

The Typical Progression a Child Makes through a State Welfare System Es

The Typical Progression a Child Makes through a State Welfare System The paper and diagram below describe the typical progression a child makes through a state welfare system. Each figure in the diagram below links to a specific decision point described in the paper, which begins immediately after the diagram. This chart provides a model, which highlights typical decision points on a child's journey through the current foster care system. Although the format is based on federal and common state law and practice, nevertheless it is only a model. Laws vary across states, as does the capacity and practices of child welfare agencies and courts to manage their caseloads. This paper describes the typical progression a child makes through a state's child welfare system. Each state's child welfare agency is responsible for ensuring the safety and well being of children. Child welfare systems have several chief components: Â · Foster care ? full-time substitute care for children removed from their parents or guardians and for whom the state has responsibility. Foster care provides food and housing to meet the physical needs of children who are removed from their homes. Â · Child protective services (CPS) ? generally a division within the child welfare agency that administers a more narrow set of services, such as receiving and responding to child abuse and neglect allegations and providing initial services to stabilize a family. Â · Juvenile and family courts ? courts with specific jurisdiction over child maltreatment and child protection cases including foster care and adoption cases. In jurisdictions without a designated family court, general trial courts hear child welfare cases along with other civil and criminal matters. Â · Other child welfare services ? in combination with the above, these services address the complex family problems associated with child abuse and neglect. They include family preservation, family reunification, adoption, guardianship, and independent living. Â · ?While 542,000 children were in foster care on September 30, 2001, 805,000 spent some time in care over the course of that year.?1 Â · ?Children in care in 2001 had been in foster care for an average of 33 months. More than 17 percent (91,217) of the children had been in care for 5 or more years.?1 Once a child is known to the child welfare agency, ... ...ip Care Families - Frequently Asked Questions (Spring 2000) and Federal Register, Vol.65, No. 16, (January 25, 2000), pp. 4032-4033. 11U.S. Department of Health and Human Services, Administration for Children & Families, National Clearinghouse on Child Abuse and Neglect Information, Foster Care National Statistics April 2001. 12U.S. Department of Health and Human Services, Administration on Children, Youth and Families, Child Maltreatment 1999: Annual Report (Washington, DC: U.S. Government Printing Office, 2001). Some states may include settings with fewer than seven children as group homes. 13U.S. Department of Health and Human Services, Administration for Children and Families, Administration for Children, Youth and Families, Program Instruction, ACYF-PI-89-09 (October 1989). 14Foster Care National Statistics April 2001 (2000b). 15Steve Christian, A Place to Call Home Adoption and Guardianship for Children in Foster Care, p.28 (National Conference of State Legislatures, 2000) 16State of Tennessee, Comptroller of the Treasury, Foster Care Independent Living Programs (1998). 171994 Green Book (Washington, DC: U.S. Government Printing Office, 1994).

Feminine Power in the Adventures of Huckleberry Finn Essay

Whether young or middle-aged, the female characters in The Adventures of Huckleberry Finn played vital roles. They were more a part of the novel’s scenic backdrop, but their function served in shaping the main character(s). The women and girls of the book were stereotypical, teachers, and â€Å"worse† than the males. The female characters were given stereotypical qualities, being depicted from an American man’s point of view. They were perceived as virtuous, innocent, helpless women, needing aid from the male characters. Women’s vulnerability can be made out in chapter eleven of the novel, where Judith Loftus confesses to wanting the assistance of Huck, â€Å"she told me to try for the next one† (Twain 59). Females occupy the back of the novel, seen as â€Å"nagging, providing inspiration, often weeping or hysterical† (Walker 139-153). You can witness this in chapter twenty-eight of the novel, where Huck stumbles upon Mary Jane Wilks, â€Å"she had stopped now, with a folded gown in her lap, and had her face in her hands, crying† (Twain 187). They possessed many assets, including: honesty, compassion, a sense of duty, innocence, and limitation; making them look powerless, as they were in the society of those days. Women were also the teachers of those days. Not only is Huck taught his education by women, but learns the ways of humanity from them as well. Some women, such as the Widow Douglas and Miss Watson, are â€Å"principal female mentors† (Walker 139-153). Huck Finn begins developing more and more traits from the females you see him interacting with. Often he â€Å"tries to run from the civilizing presence of women† (Walker 139-153). This is shown in the final chapter of the novel, â€Å"Aunt Sally she’s going to adopt me and sivilize me and I can’t stand it† (Twain 293). He is educated in school books, societal etiquette, and the Christian faith. You can find these teachings from Miss Watson in chapter one of the novel, â€Å"†¦took a set at me now, with a spelling-book. She worked me middling hard for about an hour†¦Ã¢â‚¬  (Twain 3). Lastly, the female characters were of far less import to Twain than the male characters, just as you would’ve seen in the typical culture of his day. Morally, they were better off than men, but they were powerless to society. â€Å"Both the men and the women in the novel illustrate the values of a society that has little regard for human dignity, but the female characters also embody virtues that could redeem that society if the women were empowered to do so† (Walker 139-153). The men tend to be unruly characters, while the women demonstrate high merit. My scrutiny, like Nancy Walker’s, is that the women, though supposed to have been unimportant to the novel, held essential roles. They were stereotyped teachers who had better ethics than the male characters. The book wouldn’t have been complete without them, seeing as they were a large part of Huckleberry Finn’s growth. Works Cited Walker, Nancy. â€Å"Reformers and Young Maidens: Women and Virtue in Huckleberry Finn. † Adventures of Huckleberry Finn. (1990): 139-153. Print. Twain, Mark. The Adventures of Huckleberry Finn. Austin, TX: Holt, Rinehart, and Winston. Print.

Crime And The Victims Of Crime - 1627 Words

Are those members of society who are most fearful of crime also most likely to become the victims of crime? Among society, there are many variances in people’s perceptions of safety and the threat of crime. This small essay will discuss whether members of society that are considered the most fearful of crime are accurate in their concerns and are also most likely to become victims of committed crimes. The fear of crime refers specifically to the fear and anxiety a person may feel resulting from a specific perceived threat or out of fear of potentially becoming a victim of crime, as opposed to the actual probability of becoming a victim of crime (Hale, 1996). According to Makkai and Prenzler (2014), both gender differences and age differences are variables that may affect an individual’s level of fear of becoming a victim of crime. Thus, the members of society who are considered to be the most fearful of crime are women, as well as younger and older individuals in respect to age (Davis Dossetor, 2010; Hale, 1996; Makkai Prenzler, 2014). Young individuals such as children and teenagers, and older individuals regarded as those aged 60 and over, are more likely to perceive the threat of crime as more probable and consequently be the most fearful of crime. Parker (1988) suggests that younger people’s lifestyles are a large factor in increasing their fear of crime as they regularly spend time in groups and in public places with more highly perceived rates of crime such asShow MoreRelatedVictims, Crime, And Crime Victims1579 Words   |  7 Pagesstudy of victims, especially crime victims, has created new categories of victims that had not been previously noted. 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