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A t wo-step shape reconstruction method for electromagnetic (EM) tomography is presented which uses adjoint elds and level sets. The inhomogeneous background permittivity distribution and the values of the permittivities in some penetrable obstacles are assumed to be known, and the number, sizes, shapes, and locations of these obstacles have to be reconstructed given noisy limited-view EM data. The main application we address in the paper is the imaging and monitoring of pollutant plumes in environmental cleanup sites based on cross-borehole EM data. The rst step of the reconstruction scheme makes use of an inverse scattering solver which rst recovers equivalent scattering sources for a number of experiments, and then calculates from these an approximation for the permittivity distribution in the medium. The second step uses this result as an initial guess for solving the shape reconstruction problem. A key point in this second step is the fusion of the 'level set technique' for representing the shapes of the reconstructed obstacles, and an 'adjoint eld technique' for solving the nonlinear inverse problem. In each step, a forward and an adjoint Helmholtz problem are solved based on the permittivity d i s t r ibution which corresponds to the latest best guess for the representing level set function. A correction for this level set function is then calculated directly by combining the results of these two r u n s. Numerical experiments are presented which s h o w that the derived method is able to recover one or more objects with nontrivial shapes given noisy cross-borehole EM data.

Purpose:To explore the optical and physiologic properties of normal and lesion-bearing breasts by using a combined optical and digital breast tomosynthesis (DBT) imaging system. Materials and Methods:Institutional review board approval and patient informed consent were obtained for this HIPAA-compliant study. Combined optical and tomosynthesis imaging analysis was performed in 189 breasts from 125 subjects (mean age, 56 years 6 13 [standard deviation]), including 138 breasts with negative fi ndings and 51 breasts with lesions. Threedimensional (3D) maps of total hemoglobin concentration (Hb T ), oxygen saturation (S O 2 ), and tissue reduced scattering coeffi cients were interpreted by using the coregistered DBT images. Paired and unpaired t tests were performed between various tissue types to identify signifi cant differences. Results:The estimated average bulk Hb T from 138 normal breasts was 19.2 m mol/L. The corresponding mean SO 2 was 0.73, within the range of values in the literature. A linear correlation ( R = 0.57, P , .0001) was found between Hb T and the fi broglandular volume fraction derived from the 3D DBT scans. Optical reconstructions of normal breasts revealed structures corresponding to chest-wall muscle, fi broglandular, and adipose tissues in the Hb T , SO 2 , and scattering images. In 26 malignant tumors of 0.6-2.5 cm in size, Hb T was signifi cantly greater than that in the fibroglandular tissue of the same breast ( P = .0062). Solid benign lesions ( n = 17) and cysts ( n = 8) had signifi cantly lower Hb T contrast than did the malignant lesions ( P = .025 and P = .0033, respectively). Conclusion:The optical and DBT images were structurally consistent. The malignant tumors and benign lesions demonstrated different Hb T and scattering contrasts, which can potentially be exploited to reduce the false-positive rate of conventional mammography and unnecessary biopsies. BREAST IMAGING: Combined Optical and X-ray Tomosynthesis Breast Imaging Fang et al cancers and the reduction of the number of biopsies of benign lesions, compared with stand-alone conventional mammography.Our purpose was to explore the optical and physiologic properties of normal and lesion-bearing breasts by using a combined optical and DBT imaging system. Materials and MethodsThe experimental protocols were approved by the institutional review board (Massachusetts General Hospital), and written informed consent was obtained from all subjects. The study was compliant with Health Insurance Portability and Accountability Act guidelines. Imaging InstrumentationA photograph of the combined optical and DBT imaging system and probes is shown in Figures E1 and E2 (online). The detailed confi guration of the imaging physiologic parameters, such as the concentrations of oxygenated hemoglobin (Hb O ), deoxygenated hemoglobin (Hb R ), water, and lipids ( 16 ). With DOT, nearinfrared lasers, either radiofrequencymodulated, continuous-wave or pulsed, are used to probe tissue structure noninvasively ( 13,17 ). The concentrations of the tissue ...

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypasses many difficulties with traditional level set methods, such as regularization, re-initialization and use of signed distance function. Moreover, we show that from a computational point of view, low order representation of the problem paves the path for easier use of Newton and quasi-Newton methods. Specifically for the purposes of this paper, we parameterize the level set function in terms of adaptive compactly supported radial basis functions, which used in the proposed manner provides flexibility in presenting a larger class of shapes with fewer terms. Also they provide a "narrow-banding" advantage which can further reduce the number of active unknowns at each step of the evolution. The performance of the proposed approach is examined in three examples of inverse problems, i.e., electrical resistance tomography, X-ray computed tomography and diffuse optical tomography

The selection of multiple regularization parameters is considered in a generalized L-curve framework. Multiple-dimensional extensions of the L-curve for selecting multiple regularization parameters are introduced, and a minimum distance function (MDF) is developed for approximating the regularization parameters corresponding to the generalized corner of the L-hypersurface. For the single-parameter (i.e. L-curve) case, it is shown through a model that the regularization parameters minimizing the MDF essentially maximize the curvature of the L-curve. Furthermore, for both the single-and multiple-parameter cases the MDF approach leads to a simple fixed-point iterative algorithm for computing regularization parameters. Examples indicate that the algorithm converges rapidly thereby making the problem of computing parameters according to the generalized corner of the L-hypersurface computationally tractable.

Collagen is the most prominent protein of human tissues. Its content and organization define to a large extent the mechanical properties of tissue as well as its function. Methods that have been used traditionally to visualize and analyze collagen are invasive, provide only qualitative or indirect information, and have limited use in studies that aim to understand the dynamic nature of collagen remodeling and its interactions with the surrounding cells and other matrix components. Second harmonic generation ͑SHG͒ imaging emerged as a promising noninvasive modality for providing high-resolution images of collagen fibers within thick specimens, such as tissues. In this article, we present a fully automated procedure to acquire quantitative information on the content, orientation, and organization of collagen fibers. We use this procedure to monitor the dynamic remodeling of collagen gels in the absence or presence of fibroblasts over periods of 12 or 14 days. We find that an adaptive thresholding and stretching approach provides great insight to the content of collagen fibers within SHG images without the need for user input. An additional feature-erosion and feature-dilation step is useful for preserving structure and noise removal in images with low signal. To quantitatively assess the orientation of collagen fibers, we extract the orientation index ͑OI͒, a parameter based on the power distribution of the spatial-frequency-averaged, two-dimensional Fourier transform of the SHG images. To measure the local organization of the collagen fibers, we access the Hough transform of small tiles of the image and compute the entropy distribution, which represents the probability of finding the direction of fibers along a dominant direction. Using these methods we observed that the presence and number of fibroblasts within the collagen gel significantly affects the remodeling of the collagen matrix. In the absence of fibroblasts, gels contract, especially during the first few days, in a manner that allows the fibers to remain mostly disoriented, as indicated by small OI values. Subtle changes in the local organization of fibers may be taking place as the corresponding entropy values of these gels show a small decrease. The presence of fibroblasts affects the collagen matrix in a manner that is highly dependent on their number. A low density of fibroblasts enhances the rate of initial gel contraction, but ultimately leads to degradation of collagen fibers, which start to organize in localized clumps. This degradation and reorganization is seen within the first days of incubation with fibroblasts at a high density and is followed by de novo collagen fiber deposition by the fibroblasts. These collagen fibers are more highly oriented and organized than the fibers of the original collagen gel. These initial studies demonstrate that SHG imaging in combination with automated image analysis approaches offer a noninvasive and easily implementable method for characterizing important features of the content and organization of collage...

Patch-based methods have attracted significant attention in recent years within the field of image processing for a variety of problems including denoising, inpainting, and super-resolution interpolation. Despite their prevalence for processing 2-D signals, they have received little attention in the 1-D signal processing literature. In this letter, we explore application of one such method, the nonlocal means (NLM) approach, to the denoising of biomedical signals. Using ECG as an example, we demonstrate that a straightforward NLM-based denoising scheme provides signal-to-noise ratio improvements very similar to state of the art wavelet-based methods, while giving ~3 × or greater reduction in metrics measuring distortion of the denoised waveform.

Multiple Hypothesis Video Segmentation (MHVS) is a method for the unsupervised photometric segmentation of video sequences. MHVS segments arbitrarily long video streams by considering only a few frames at a time, and handles the automatic creation, continuation and termination of labels with no user initialization or supervision. The process begins by generating several pre-segmentations per frame and enumerating multiple possible trajectories of pixel regions within a short time window. After assigning each trajectory a score, we let the trajectories compete with each other to segment the sequence. We determine the solution of this segmentation problem as the MAP labeling of a higher-order random field. This framework allows MHVS to achieve spatial and temporal long-range label consistency while operating in an on-line manner. We test MHVS on several videos of natural scenes with arbitrary camera and object motion.