Extrapolation Algorithm Research Articles

An improved GVF snake based breast region extrapolation scheme for digital mammograms

To accurately extrapolate the breast region from a mammogram is a crucial stage of breast mass analysis. It significantly influences the overall analysis accuracy and processing speed of the whole breast mass analysis. In this paper, a novel edge map adjusting gradient vector flow snake (EMA GVF snake) algorithm for extrapolation of breast region from mammograms is proposed. In the proposed algorithm, the median filter is used to filter out the noise in a mammogram, the scale down stage is used to resize down the mammogram size (hence speeding up the extrapolation). The binarization processing stage and the morphological erosion processing stage are used to find a rough breast border. Then a novel gradient adjusting stage is applied to get a modified edge map and the gradient vector flow snake (GVF snake) is used to get the accurate breast border from the rough breast border. The proposed algorithm is tested on 322 digital mammograms from the Mammogram Image Analysis Society database. The mean error function, misclassification error function and the relative foreground area error function are conducted to evaluate the results of the detected breast border and the extracted breast region. Experimental results show that the breast border extrapolated by the proposed algorithm approximately follows the breast border extrapolated by an expert radiologist. Experimental results also show that the proposed algorithm is more robust and precise than the traditional GVF snake scheme for the breast extrapolation on mammograms.

Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods

The accuracy of numerical solutions near singular points is crucial for numerical methods. In this paper we develop an efficient mechanical quadrature method (MQM) with high accuracy. The following advantages of MQM show that it is very promising and beneficial for practical applications: (1) the $ O(h_{\rm {max}}^{3})$ convergence rate; (2) the $O(h_{\rm {max}}^{5})$ convergence rate after splitting extrapolation; (3) Cond = $O(h_{\rm {min}}^{-1})$ ; (4) the explicit discrete matrix entries. In this paper, the above theoretical results are briefly addressed and then verified by numerical experiments. The solutions of MQM are more accurate than those of other methods. Note that for the discontinuous model in Li et al. (Eng Anal Bound Elem 29:59---75, 2005), the highly accurate solutions of MQM may even compete with those of the collocation Trefftz method.

Ultrasonic Positioning Using Curve-Fitting Extrapolation and Redundant Information Fusion

To study the problem of high precision, the reason why error appears in the ultrasonic positioning process is analyzed. To decrease the effect of error, this paper raises the algorithm of curve-fitting extrapolation and redundant information fusion. The experiment and contrast on precision between this algorithm and other classical ones demonstrate that, the new algorithm could effectively control measurement errors and raise the precision of ultrasonic positioning.

Splitting extrapolation algorithms for solving the boundary integral equations of Steklov problems on polygons by mechanical quadrature methods

By the potential theory, Steklov eigenvalue problems are converted into boundary integral equations (BIEs). The singularities at corners and in the integral kernels are studied in this paper. Mechanical quadrature methods (MQMs) are presented to obtain approximations with a high accuracy order O ( h 3 ) . Moreover, the mechanical quadrature methods are simple without any singularly integral computation. Since the asymptotic expansions of the errors with the power O ( h 3 ) are shown, the high accuracy order O ( h 5 ) can be achieved for the solutions by using the splitting extrapolation algorithms (SEAs). A posteriori error estimate can also be obtained for self-adaptive algorithms. The efficiency of the algorithms is illustrated by examples.

Passive Millimeter-wave Image Restoration Based on Improved algorithm of Nonlinear Extrapolation in Frequency Space

Passive Millimeter-wave Image Restoration Based on Improved algorithm of Nonlinear Extrapolation in Frequency Space

Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods

We study the numerical solution procedure for two-dimensional Laplace's equation subjecting to non-linear boundary conditions. Based on the potential theory, the problem can be converted into a nonlinear boundary integral equations. Mechanical quadrature methods are presented for solving the equations, which possess high accuracy order O(h 3) and low computing complexities. Moreover, the algorithms of the mechanical quadrature methods are simple without any integration computation. Harnessing the asymptotical compact theory and Stepleman theorem, an asymptotic expansion of the errors with odd powers is shown. Based on the asymptotic expansion, the h 3??Richardson extrapolation algorithms are used and the accuracy order is improved to O(h 5). The efficiency of the algorithms is illustrated by numerical examples.

Three-dimensional noisy image restoration using filtered extrapolation and deconvolution

The problem of restoration in fluorescence microscopy has to deal at the same time with blurring and photon noise. Their combined effects corrupt the image by inserting elements that do not belong to the real object and distort the contrast. This hinders the possibility of using the images for visualization, recognition, and analysis using the three-dimensional data. The algorithms developed to restore the lost frequencies and perform band extrapolation, in general, assume absence of noise or an additive noise. This paper presents a restoration approach through band extrapolation and deconvolution that deals with the noise. An extrapolation algorithm using constraints on both spatial and frequency domains with a smoothing operator were combined with the Richardson-Lucy iterative algorithm. The results of the method for simulated data are compared with those obtained by the original Richardson-Lucy algorithm and also regularized by Total Variation. The extrapolation of frequencies is also analyzed both in synthetic and in real images. The method improved the results with higher signal-to-noise ratio and quality index values, performing band extrapolation, and achieving a better visualization of the 3D structures.

A Fast Algorithm for Selective Signal Extrapolation with Arbitrary Basis Functions

Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive and, up to now, efficient implementations exist only for basis function sets that emanate from discrete transforms. Within the scope of this contribution, a novel efficient solution for Selective Extrapolation is presented for utilization with arbitrary basis functions. The proposed algorithm mathematically behaves identically to the original Selective Extrapolation, but is several decades faster. Furthermore, it is able to outperform existent fast transform domain algorithms which are limited to basis function sets that belong to the corresponding transform. With that, the novel algorithm allows for an efficient use of arbitrary basis functions, even if they are only numerically defined.

Reconstruction from truncated projections using mixed extrapolations of exponential and quadratic functions

In computer tomography (CT), truncated projections are produced due to scanning large objects with a detector that is limited in width. Applying filtered back-projection(FBP) method directly to truncated projections, the reconstructed image will contain truncation artifacts - bright rings on the boundary of region of interest (ROI). Extrapolation algorithms can be used to reduce the truncation artifacts; however extrapolations are usually double the length of the projection data; resulting in an increased calculation time. This paper introduces mixed extrapolation, which is a combination of exponential and quadratic extrapolation. It is proven that doubling the length of the projection data for the mixed extrapolation can be avoided. The projections were extrapolated according to the boundary values and their derivatives. The algorithm achieves equivalence to the extrapolation approach with negligible increased calculation time. Supplementary functions are introduced in order to simplify the calculations. These functions can be calculated prior to extrapolation process, hence the calculation time is significantly reduced. The calculation times are compared between fast extrapolation introduced in this paper and normal extrapolation with doubling the length of projection data.

Extracting Red Edge Position Parameters from Ground- and Space-Based Hyperspectral Data for Estimation of Canopy Leaf Nitrogen Concentration in Rice

To realize non-destructive and real-time monitoring of crop nitrogen status for precision management in rice fertilization, we characterized the reflectance spectra in the red edge area from ground- and space-based data, and quantified the relationships between the red edge position (REP) derived from different algorithms and canopy leaf nitrogen concentrations (LNC) at various nitrogen rates in four seasons in various cultivars of field-grown rice (Oryza sativa L.). The results showed that the spectrum in the red edge area was significantly affected by the nitrogen level and cultivar type, and “three-peak” feature could be observed in the first derivative spectrum in this area. Traditional REP (maximum value of the first derivative spectra in red-edge region) was not sensitive to canopy LNC because of the three-peak property, but the REPs based on inverted Gaussian fitting, linear four-point interpolation, linear extrapolation and adjusted linear extrapolation generated continuous REP values, and could be used for estimating canopy LNC. REP from a three-point Lagrangian interpolation with three first-derivative bands (690 nm, 700 nm and 705 nm) had a good relationship with canopy LNC. Among the six REP approaches, REP based on adjusted linear extrapolation algorithm was found to have the best relations with canopy LNCs in Hyperion image data. Comparison of the different REPs with both ground-based and space-borne hyperspectral data indicated that the adjusted linear extrapolation method (755FD730+675FD700)/(FD730+FD700) proposed here gave the best prediction of canopy LNC. This simple and reliable REP approach to monitoring canopy LNC in rice requires further verification with other hyperspectral sensors and crop types.

High accuracy eigensolution and its extrapolation for potential equations

From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations (BIEs) with the logarithmic singularity. In this paper, mechanical quadrature methods (MQMs) are presented to obtain the eigensolutions that are used to solve Laplace’s equations. The MQMs possess high accuracy and low computation complexity. The convergence and the stability are proved based on Anselone’s collective and asymptotical compact theory. An asymptotic expansion with odd powers of the errors is presented. By the h 3-Richardson extrapolation algorithm (EA), the accuracy order of the approximation can be greatly improved, and an a posteriori error estimate can be obtained as the self-adaptive algorithms. The efficiency of the algorithm is illustrated by examples.

An Improved Error Concealment Algorithm for Wireless Video Applications

This paper develops a new error concealment algorithm for the whole-frame losses in wireless video transmission based on H.264/AVC.At first,we propose a forward motion vector extrapolation algorithm based on variable-size block motion vector estimation to obtain the motion vector field of the loss frame without yielding the hole problems. Then, we partition the missing frame into several object regions by clustering the motion vectors, furthermore, we apply median filter to reconstruct the motion vectors for hole areas based on the reliabilities of neighboring motion vectors. Finally, all macroblocks in the lost frame are estimated by using the extrapolated motion vectors. Experimental results show that the proposed algorithm provides better image quality than conventional methods both objectively and subjectively.

Highlights of This Issue

The ability to predict the efficacy of molecularly targeted therapies for non-small cell lung cancer (NSCLC) for an individual patient remains problematic. Nagji and colleagues used the refined coexpression extrapolation (COXEN) algorithm to identify tumor biomarkers that predict drug sensitivity and therapeutic efficacy in NSCLC to Vorinostat (histone deacetylase inhibitor) and Velcade (proteasome inhibitor). Importantly, they provide an in silico method to generate biomarkers that predict tumor sensitivity to novel molecularly targeted therapies. Use of this refined COXEN methodology has significant implications for the a priori examination of targeted therapies to more effectively streamline subsequent clinical trial design and cost.Since αvβ3 integrin plays a key role in angiogenesis and metastasis of human tumors, ligands against this integrin are potentially useful in targeted therapy and cancer imaging. Xiao and colleagues report that a novel RGD peptide ligand, LXW7 with a built-in handle, was identified using OBOC combinatorial chemistry. LXW7 demonstrated high targeting efficacy and specificity for the αvβ3 integrin expressed in tumor cells. Moreover, LXW7 permits easier functionalization for payload conjugation without attenuating the binding affinity of the peptide compared with RGD cyclopentapeptide ligands. LXW7, therefore, has great potential as a highly efficient peptide ligand for targeted imaging and drug delivery.Non-small cell lung cancer (NSCLC) with an activating mutation of the epidermal growth factor receptor (EGFR) ultimately develops resistance to EGFR tyrosine kinase inhibitors (TKI). Okamoto and colleagues show that EGFR mutation–positive NSCLC (HCC827) cells engineered to stably overexpress HGF (HCC827-HGF) exhibit gefitinib resistance. TAK-701, a humanized monoclonal antibody to HGF, in combination with gefitinib suppressed their growth in HCC827-HGF cells both in vitro and in vivo. Our findings suggest that the addition of TAK-701 to gefitinib is a promising strategy to overcome EGFR-TKI resistance induced by HGF in NSCLC with an activating EGFR mutation.Aurora A kinase (AAK), a protein kinase critical for tumor proliferation and survival, is a novel target for cancer treatment. MLN8054, an oral small-molecule AAK inhibitor, produces broad preclinical antitumor activity. In this Phase I study, Macarulla and colleagues evaluated safety, pharmacokinetics, and pharmacodynamics in serial tumor and skin biopsies. Total daily doses of 70 or 80 mg led to marked changes in mitotic cell chromosome alignment and spindle bipolarity in some patients. These results provide evidence for the dominant mechanism to inhibit AAK and support ongoing efforts to target this enzyme in the clinical treatment setting.

Error and extrapolation of a compact LOD method for parabolic differential equations

This paper is concerned with a compact locally one-dimensional (LOD) finite difference method for solving two-dimensional nonhomogeneous parabolic differential equations. An explicit error estimate for the finite difference solution is given in the discrete infinity norm. It is shown that the method has the accuracy of the second-order in time and the fourth-order in space with respect to the discrete infinity norm. A Richardson extrapolation algorithm is developed to make the final computed solution fourth-order accurate in both time and space when the time step equals the spatial mesh size. Numerical results demonstrate the accuracy and the high efficiency of the extrapolation algorithm.

A composite approach of radar echo extrapolation based on TREC vectors in combination with model-predicted winds

Extending the lead time of precipitation nowcasts is vital to improvements in heavy rainfall warning, flood mitigation, and water resource management. Because the TREC vector (tracking radar echo by correlation) represents only the instantaneous trend of precipitation echo motion, the approach using derived echo motion vectors to extrapolate radar reflectivity as a rainfall forecast is not satisfactory if the lead time is beyond 30 minutes. For longer lead times, the effect of ambient winds on echo movement should be considered. In this paper, an extrapolation algorithm that extends forecast lead times up to 3 hours was developed to blend TREC vectors with model-predicted winds. The TREC vectors were derived from radar reflectivity patterns in 3 km height CAPPI (constant altitude plan position indicator) mosaics through a cross-correlation technique. The background steering winds were provided by predictions of the rapid update assimilation model CHAF (cycle of hourly assimilation and forecast). A similarity index was designed to determine the vertical level at which model winds were applied in the extrapolation process, which occurs via a comparison between model winds and radar vectors. Based on a summer rainfall case study, it is found that the new algorithm provides a better forecast.

Cross rules of some extrapolation algorithms

In this paper, we present the cross rules of some extrapolation algorithms. These new cross rules are similar in their spirit to the cross rule for the scalar ε-algorithm and the ϱ-algorithm. The first interest of such rules is that, in the algorithms for implementing sequence transformations for the acceleration of the convergence, they allow us to compute only the quantities which have a signification for extrapolation and to jump over the intermediate ones. The second interest comes out from the link between convergence acceleration methods, soliton theory and discrete integrable systems. In some cases, cross rules directly lead to physically significant integrable systems. For example, the cross rule of the confluent qd-algorithm leads to the celebrated Toda equation, which is known to have physical applications.

Advanced quadrature methods and splitting extrapolation algorithms for first kind boundary integral equations of Laplace's equation with discontinuity solutions

The Laplace equation can be transformed to the first kind boundary integral equations (BIEs), and the corner and discontinuity singularity of Laplace's equation can be studied by the open arcs of the BIEs. For the first kind BIEs, there exist the Galerkin method (GM) and the collocation method (CM); but they suffer in low convergence. The advanced (i.e., the mechanical) quadrature methods (AQMs) and the splitting extrapolation methods (SEMs) originated in [16,17] are proposed in Huang et al. [15] for first kind BIEs with open arcs, to achieve O( h 3) or even O( h 5) convergence, and the excellent stability with Cond. = O( h −1), where h is the uniform meshspacing, accompanied with the strict analysis. Moreover, the algorithms of AQMs and the SEMs are simple without any integration computation. Hence the AQMs and the SEMs are superior to the existing methods, such as GM and CM. A challenging discontinuity model of Laplace's equation is proposed in Li et al. [20], and the collocation Trefftz method (CTM) is used to give highly accurate solutions. For the AQMs and the SEMs, the strict theoretical analysis is given in [15], and the discontinuity model [20] is dealt with in this paper, to also achieve highly accurate solutions. The numerical solutions in this paper display that the AQMs and the SEMs are significant not only to the first kind BIEs with the open arc singularity, but also to Laplace's equation with highly strong singularity such as the discontinuity of solutions. Moreover, the link of the first kind BIEs with open arcs and the Laplace equation with discontinuity solutions are explored clearly, to display the significance of the proposed algorithms; this paper strengthens the first kind BIEs and its engineering applications.

A Novel Integration Method for Weak Singularity Arising in Two-Dimensional Scattering Problems

In this paper, we introduce a novel mechanical quadrature method for an efficient solution of weakly singular integral equations arising in two-dimensional electromagnetic scattering problems. This approach is based on and adapted from the recently proposed mechanical quadrature methods in [Extrapolation algorithms for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods, SIAM J. Sci. Comput., vol. 31, 4115-4129, 2009]. We report experiments for solving TM-polarized induced currents and scattered fields to show its superiority to the classical method of moments when accuracy is a concern. Moreover, additional numerical experiments made with an extrapolation algorithm suggest that the accuracy of the present method can be further improved dramatically by means of the extrapolation algorithm to some extent.

A gene expression algorithm for the prediction of platinum sensitivity in ovarian cancer.

5021 Background: Despite advances in radical surgery and chemotherapy delivery, ovarian cancer is the most lethal gynecologic malignancy. In vitro models predicting chemosensitivity rely on cellular phenotypes and are hampered by the extrapolation of data from culture to clinic. Gene expression models can predict therapeutic responses without these constraints. We tested our gene based co-expression extrapolation (COXEN) algorithm on a cohort of 65 ovarian cancer patients to assess its clinical utility. Methods: COXEN is an in silico algorithm that predicts chemosensitivity of tumors based on genomic expression signatures and has been reported previously. In brief, NCI- 60 cell lines were used to identify candidate drug sensitivity biomarkers for carboplatin and paclitaxel. Candidate biomarkers were then narrowed by examining concordant expression patterns between cell lines and a historical set of ovarian cancer patients. Biomarkers were further triaged by examining expression patterns of frozen and formalin-fixed paraffin embedded (FFPE) tissue samples. Models were refined using an independent cohort from which the final prediction models were obtained. To evaluate the clinical utility of COXEN in ovarian cancer, we performed genome-wide profiling on FFPE samples of 65 patients obtained prior to adjuvant chemotherapy. We then retrospectively applied COXEN to this cohort to evaluate the predictive success. Results: COXEN correctly stratified platinum sensitive and resistant patients (p = 0.019) with sensitivity = 93%, specificity = 33%, PPV = 65%, and NPV = 78%. Paclitaxel response was also significantly stratified (p = 0.033) with sensitivity = 96%, specificity = 26%, PPV = 61%, and NPV = 86%. Models for platinum-taxane combination demonstrated a significant survival difference between the predicted responders and nonresponders with median survival of 12.9 months vs. 8.1 months (p = 0.045). Conclusions: COXEN successfully predicted platinum resistance and reliably discriminated taxane response in this retrospective cohort. Prediction of platinum response is clinically relevant and, if reliable, could alter primary management of ovarian cancer. Prospective evaluation of the COXEN model is underway. Author Disclosure Employment or Leadership Position Consultant or Advisory Role Stock Ownership Honoraria Research Funding Expert Testimony Other Remuneration Key Genomics Key Genomics

The COXEN Principle: Translating Signatures of In vitro Chemosensitivity into Tools for Clinical Outcome Prediction and Drug Discovery in Cancer

Substantial effort has been devoted to in vitro testing of candidate chemotherapeutic agents. In particular, the United States National Cancer Institute Developmental Therapeutics Program (NCI-DTP) Human Tumor Cell Line Screen has screened hundreds of thousands of compounds and extracts, for which data on more than 40,000 compounds tested on a panel of 60 cancer cell lines (NCI-60) are publically available. In tandem, gene expression profiling has brought about a sea change in our understanding of cancer biology, allowing discovery of biomarkers or signatures able to characterize, classify, and prognosticate clinical behavior of human tumors. Recent studies have used tumor profiling matched to clinical trial outcome data to derive gene expression models predicting therapeutic outcomes, though such efforts are costly, time-consuming, tumor type-specific, and not amenable to rare diseases. Furthermore, addition of new or established drugs to multidrug combinations in which such models are already available requires the entire model to be re-derived. Can the aforementioned in vitro testing platform, coupled to the universal language of genomics, be used to develop, a priori, gene expression models predictive of clinical outcomes? Recent advances, including the CO-eXpression ExtrapolatioN (COXEN) algorithm, suggest that development of these models may be possible and raise important implications for future trial design and drug discovery.