Some Paranormed Difference Sequence Spaces of Order mm Derived by Generalized Means and Compact Operators

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{(m)})$ to $l_{\infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space $l_{p}(r, s, t ;\Delta^{(m)})$ by applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some results. 20 pages. arXiv admin note: substantial text overlap with arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588

A spatially constrained probabilistic model for robust image segmentation

In general, the hidden Markov random field (HMRF) represents the class label distribution of an image in probabilistic model based segmentation. The class label distributions provided by existing HMRF models consider either the number of neighboring pixels with similar class labels or the spatial distance of neighboring pixels with dissimilar class labels. Also, this spatial information is only considered for estimation of class labels of the image pixels, while its contribution in parameter estimation is completely ignored. This, in turn, deteriorates the parameter estimation, resulting in sub-optimal segmentation performance. Moreover, the existing models assign equal weightage to the spatial information for class label estimation of all pixels throughout the image, which, create significant misclassification for the pixels in boundary region of image classes. In this regard, the paper develops a new clique potential function and a new class label distribution, incorporating the information of image class parameters. Unlike existing HMRF model based segmentation techniques, the proposed framework introduces a new scaling parameter that adaptively measures the contribution of spatial information for class label estimation of image pixels. The importance of the proposed framework is depicted by modifying the HMRF based segmentation methods. The advantage of proposed class label distribution is also demonstrated irrespective of the underlying intensity distributions. The comparative performance of the proposed and existing class label distributions in HMRF model is demonstrated both qualitatively and quantitatively for brain MR image segmentation, HEp-2 cell delineation, natural image and object segmentation

Noninvasive depth estimation using tissue optical properties and a dual-wavelength fluorescent molecular probe in vivo

Translation of fluorescence imaging using molecularly targeted imaging agents for real-time assessment of surgical margins in the operating room requires a fast and reliable method to predict tumor depth from planar optical imaging. Here, we developed a dual-wavelength fluorescent molecular probe with distinct visible and near-infrared excitation and emission spectra for depth estimation in mice and a method to predict the optical properties of the imaging medium such that the technique is applicable to a range of medium types. Imaging was conducted at two wavelengths in a simulated blood vessel and an in vivo tumor model. Although the depth estimation method was insensitive to changes in the molecular probe concentration, it was responsive to the optical parameters of the medium. Results of the intra-tumor fluorescent probe injection showed that the average measured tumor sub-surface depths were 1.31 ± 0.442 mm, 1.07 ± 0.187 mm, and 1.42 ± 0.182 mm, and the average estimated sub-surface depths were 0.97 ± 0.308 mm, 1.11 ± 0.428 mm, 1.21 ± 0.492 mm, respectively. Intravenous injection of the molecular probe allowed for selective tumor accumulation, with measured tumor sub-surface depths of 1.28 ± 0.168 mm, and 1.50 ± 0.394 mm, and the estimated depths were 1.46 ± 0.314 mm, and 1.60 ± 0.409 mm, respectively. Expansion of our technique by using material optical properties and mouse skin optical parameters to estimate the sub-surface depth of a tumor demonstrated an agreement between measured and estimated depth within 0.38 mm and 0.63 mm for intra-tumor and intravenous dye injections, respectively. Our results demonstrate the feasibility of dual-wavelength imaging for determining the depth of blood vessels and characterizing the sub-surface depth of tumors in vivo

Inferring Biological Structures from Super-Resolution Single Molecule Images Using Generative Models

Localization-based super resolution imaging is presently limited by sampling requirements for dynamic measurements of biological structures. Generating an image requires serial acquisition of individual molecular positions at sufficient density to define a biological structure, increasing the acquisition time. Efficient analysis of biological structures from sparse localization data could substantially improve the dynamic imaging capabilities of these methods. Using a feature extraction technique called the Hough Transform simple biological structures are identified from both simulated and real localization data. We demonstrate that these generative models can efficiently infer biological structures in the data from far fewer localizations than are required for complete spatial sampling. Analysis at partial data densities revealed efficient recovery of clathrin vesicle size distributions and microtubule orientation angles with as little as 10% of the localization data. This approach significantly increases the temporal resolution for dynamic imaging and provides quantitatively useful biological information