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Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] × [-2, 2] with constraints for biaxial symmetry, diagonal (or 90° rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-SPCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply. [ABSTRACT FROM AUTHOR]

The continuous interest in non-targeted profiling induced the development of tools for automated cross-sample analysis. Such tools were found to be selective or not comprehensive thus delivering a biased view on the qualitative/quantitative peak distribution across 2D sample chromatograms. Therefore, the performance of non-targeted approaches needs to be critically evaluated. This study focused on the development of a validation procedure for non-targeted, peak-based, GC×GC-MS data profiling. The procedure introduced performance parameters such as specificity, precision, accuracy, and uncertainty for a profiling method known as Comprehensive Template Matching. The performance was assessed by applying a three-week validation protocol based on CITAC/EURACHEM guidelines. Optimized ¹D and ²D retention times search windows, MS match factor threshold, detection threshold, and template threshold were evolved from two training sets by a semi-automated learning process. The effectiveness of proposed settings to consistently match 2D peak patterns was established by evaluating the rate of mismatched peaks and was expressed in terms of results accuracy. The study utilized 23 different 2D peak patterns providing the chemical fingerprints of raw and roasted hazelnuts (Corylus avellana L.) from different geographical origins, of diverse varieties and different roasting degrees. The validation results show that non-targeted peak-based profiling can be reliable with error rates lower than 10% independent of the degree of analytical variance. The optimized Comprehensive Template Matching procedure was employed to study hazelnut roasting profiles and in particular to find marker compounds strongly dependent on the thermal treatment, and to establish the correlation of potential marker compounds to geographical origin and variety/cultivar and finally to reveal the characteristic release of aroma active compounds., (Copyright © 2012 Elsevier B.V. All rights reserved.)

This review surveys different approaches for generating features from comprehensive two-dimensional chromatography for non-targeted cross-sample analysis. The goal of non-targeted cross-sample analysis is to discover relevant chemical characteristics (such as compositional similarities or differences) from multiple samples. In non-targeted analysis, the relevant characteristics are unknown, so individual features for all chemical constituents should be analyzed, not just those for targeted or selected analytes. Cross-sample analysis requires matching the corresponding features that characterize each constituent across multiple samples so that relevant characteristics or patterns can be recognized. Non-targeted, cross-sample analysis requires generating and matching all features across all samples. Applications of non-targeted cross-sample analysis include sample classification, chemical fingerprinting, monitoring, sample clustering, and chemical marker discovery. Comprehensive two-dimensional chromatography is a powerful technology for separating complex samples and so is well suited for non-targeted cross-sample analysis. However, two-dimensional chromatographic data is typically large and complex, so the computational tasks of extracting and matching features for pattern recognition are challenging. This review examines five general approaches that researchers have applied to these difficult problems: visual image comparisons, datapoint feature analysis, peak feature analysis, region feature analysis, and peak-region feature analysis., (Copyright © 2011 Elsevier B.V. All rights reserved.)

Comprehensive two-dimensional gas chromatography (GC×GC) is a powerful technology for separating complex samples. The typical goal of GC×GC peak detection is to aggregate data points of analyte peaks based on their retention times and intensities. Two techniques commonly used for two-dimensional peak detection are the two-step algorithm and the watershed algorithm. A recent study [4] compared the performance of the two-step and watershed algorithms for GC×GC data with retention-time shifts in the second-column separations. In that analysis, the peak retention-time shifts were corrected while applying the two-step algorithm but the watershed algorithm was applied without shift correction. The results indicated that the watershed algorithm has a higher probability of erroneously splitting a single two-dimensional peak than the two-step approach. This paper reconsiders the analysis by comparing peak-detection performance for resolved peaks after correcting retention-time shifts for both the two-step and watershed algorithms. Simulations with wide-ranging conditions indicate that when shift correction is employed with both algorithms, the watershed algorithm detects resolved peaks with greater accuracy than the two-step method., (Copyright © 2011 Elsevier B.V. All rights reserved.)

We successfully detected halogenated compounds from several kinds of environmental samples by using a comprehensive two-dimensional gas chromatograph coupled with a tandem mass spectrometer (GC×GC-MS/MS). For the global detection of organohalogens, fly ash sample extracts were directly measured without any cleanup process. The global and selective detection of halogenated compounds was achieved by neutral loss scans of chlorine, bromine and/or fluorine using an MS/MS. It was also possible to search for and identify compounds using two-dimensional mass chromatograms and mass profiles obtained from measurements of the same sample with a GC×GC-high resolution time-of-flight mass spectrometer (HRTofMS) under the same conditions as those used for the GC×GC-MS/MS. In this study, novel software tools were also developed to help find target (halogenated) compounds in the data provided by a GC×GC-HRTofMS. As a result, many dioxin and polychlorinated biphenyl congeners and many other halogenated compounds were found in fly ash extract and sediment samples. By extracting the desired information, which concerned organohalogens in this study, from huge quantities of data with the GC×GC-HRTofMS, we reveal the possibility of realizing the total global detection of compounds with one GC measurement of a sample without any pre-treatment., (Copyright © 2011 Elsevier B.V. All rights reserved.)

This paper describes informatics for cross-sample analysis with comprehensive two-dimensional gas chromatography (GCxGC) and high-resolution mass spectrometry (HRMS). GCxGC-HRMS analysis produces large data sets that are rich with information, but highly complex. The size of the data and volume of information requires automated processing for comprehensive cross-sample analysis, but the complexity poses a challenge for developing robust methods. The approach developed here analyzes GCxGC-HRMS data from multiple samples to extract a feature template that comprehensively captures the pattern of peaks detected in the retention-times plane. Then, for each sample chromatogram, the template is geometrically transformed to align with the detected peak pattern and generate a set of feature measurements for cross-sample analyses such as sample classification and biomarker discovery. The approach avoids the intractable problem of comprehensive peak matching by using a few reliable peaks for alignment and peak-based retention-plane windows to define comprehensive features that can be reliably matched for cross-sample analysis. The informatics are demonstrated with a set of 18 samples from breast-cancer tumors, each from different individuals, six each for Grades 1-3. The features allow classification that matches grading by a cancer pathologist with 78% success in leave-one-out cross-validation experiments. The HRMS signatures of the features of interest can be examined for determining elemental compositions and identifying compounds., (Copyright © 2010 Elsevier B.V. All rights reserved.)

This study examined how advanced fingerprinting methods (i.e., non-targeted methods) provide reliable and specific information about groups of samples based on their component distribution on the GC x GC chromatographic plane. The volatile fractions of roasted hazelnuts (Corylus avellana L.) from nine different geographical origins, comparably roasted for desirable flavor and texture, were sampled by headspace-solid phase micro extraction (HS-SPME) and then analyzed by GC x GC-qMS. The resulting patterns were processed by: (a) "chromatographic fingerprinting", i.e., a pattern recognition procedure based on retention-time criteria, where peaks correspondences were established through a comprehensive peak pattern covering the chromatographic plane; and (b) "comprehensive template matching" with reliable peak matching, where peak correspondences were constrained by retention time and MS fragmentation pattern similarity criteria. Fingerprinting results showed how the discrimination potential of GC x GC can be increased by including in sample comparisons and correlations all the detected components and, in addition, provide reliable results in a comparative analysis by locating compounds with a significant role. Results were completed by a chemical speciation of volatiles and sample profiling was extended to known markers whose distribution can be correlated to sensory properties, geographical origin, or the effect of thermal treatment on different classes of compounds. The comprehensive approach for data interpretation here proposed may be useful to assess product specificity and quality, through measurable parameters strictly and consistently correlated to sensory properties and origin., (Copyright 2010 Elsevier B.V. All rights reserved.)

The present study examines the ability of targeted and non-targeted methods to provide specific and complementary information on groups of samples on the basis of their component distribution on the two-dimensional gas chromatography (GCxGC) plane. The volatile fraction of Arabica green and roasted coffee samples differing in geographical origins and roasting treatments and the volatile fraction from juniper needles, sampled by headspace-solid phase microextraction, were analyzed by GCxGC-qMS and sample profiles processed by different approaches. In the target analysis profiling, samples submitted to different roasting cycles and/or differing in origin and post-harvest treatment are characterized on the basis of known constituents (botanical, technological, and/or aromatic markers). This approach provides highly reliable results on quali-quantitative compositional differences because of the authentic standard confirmation, extending and improving the specificity of the comparative procedure to trace and minor components. On the other hand, non-targeted data-processing methods (e.g., direct image comparison and template-based fingerprinting) include in the sample comparisons and correlations all detected sample components, offering an increased discrimination potential by identifying compounds that are comparatively significant but not known targets. Results demonstrate the ability of GCxGC to explore in depth the complexity of samples and emphasize the advantages of a comprehensive and multidisciplinary approach to improve the level of information provided by GCxGC separation.

Comprehensive two-dimensional liquid chromatography (LCxLC) generates information-rich but complex peak patterns that require automated processing for rapid chemical identification and classification. This paper describes a powerful approach and specific methods for peak pattern matching to identify and classify constituent peaks in data from LCxLC and other multidimensional chemical separations. The approach records a prototypical pattern of peaks with retention times and associated metadata, such as chemical identities and classes, in a template. Then, the template pattern is matched to the detected peaks in subsequent data and the metadata are copied from the template to identify and classify the matched peaks. Smart Templates employ rule-based constraints (e.g., multispectral matching) to increase matching accuracy. Experimental results demonstrate Smart Templates, with the combination of retention-time pattern matching and multispectral constraints, are accurate and robust with respect to changes in peak patterns associated with variable chromatographic conditions.

Two computationally efficient methods for superresolution reconstruction and restoration of microscanning imaging systems are presented. Microscanning creates multiple low-resolution images with slightly different sample-scene phase shifts. The digital processing methods developed here combine the low-resolution images to produce an image with higher pixel resolution (i.e., superresolution) and higher fidelity. The methods implement reconstruction to increase resolution and restoration to improve fidelity in one-pass convolution with a small kernel. One method uses a small-kernel Wiener filter and the other method uses a parametric cubic convolution filter. Both methods are based on an end-to-end, continuous-discrete-continuous microscanning imaging system model. Because the filters are constrained to small spatial kernels they can be efficiently applied by convolution and are amenable to adaptive processing and to parallel processing. Experimental results with simulated imaging and with real microscanned images indicate that the small-kernel methods efficiently and effectively increase resolution and fidelity.

This paper investigates methods for comparing datasets produced by comprehensive two-dimensional gas chromatography (GC x GC). Chemical comparisons are useful for process monitoring, sample classification or identification, correlative determinations, and other important tasks. GC x GC is a powerful new technology for chemical analysis, but methods for comparative visualization must address challenges posed by GC x GC data: inconsistency and complexity. The approach extends conventional techniques for image comparison by utilizing specific characteristics of GC x GC data and developing new methods for comparative visualization and analysis. The paper describes techniques that register (or align) GC x GC datasets to remove retention-time variations; normalize intensities to remove sample amount variations; compute differences in local regions to remove slight misregistrations and differences in peak shapes; employ color (hue), intensity, and saturation to simultaneously visualize differences and values; and use tools for masking, three-dimensional visualization, and tabular presentation with controls for graphical highlights to significantly improve comparative analysis of GC x GC datasets. Experimental results indicate that the comparative methods preserve chemical information and support qualitative and quantitative analyses.

Identifying compounds of interest for peaks in data generated by comprehensive two-dimensional gas chromatography (GC x GC) is a critical analytical task. Manually identifying compounds is tedious and time-consuming. An alternative is to use pattern matching. Pattern matching identifies compounds by matching previously observed patterns with known peaks to newly observed patterns with unidentified peaks. The fundamental difficulty of pattern matching comes from peak pattern distortions that are caused by differences in data acquisition conditions. This paper investigates peak pattern variations related to varying oven temperature ramp rate and inlet gas pressure and evaluates two types of affine transformations for matching peak patterns. The experimental results suggest that, over the experimental ranges, the changes in temperature ramp rate generate non-linear pattern variations and changes in gas pressure generate nearly linear pattern variations. The results indicate the affine transformations can largely remove the pattern variations and can be used for applications such as pattern matching and normalizing retention times to retention indices.

This paper describes a language for expressing criteria for chemical identification with comprehensive two-dimensional gas chromatography paired with mass spectrometry (GC x GC-MS) and presents computer-based tools implementing the language. The Computer Language for Indentifying Chemicals (CLIC) allows expressions that describe rules (or constraints) for selecting chemical peaks or data points based on multi-dimensional chromatographic properties and mass spectral characteristics. CLIC offers chromatographic functions of retention times, functions of mass spectra, numbers for quantitative and relational evaluation, and logical and arithmetic operators. The language is demonstrated with the compound-class selection rules described by Welthagen et al. [W. Welthagen, J. Schnelle-Kreis, R. Zimmermann, J. Chromatogr. A 1019 (2003) 233-249]. A software implementation of CLIC provides a calculator-like graphical user-interface (GUI) for building and applying selection expressions. From the selection calculator, expressions can be used to select chromatographic peaks that meet the criteria or create selection chromatograms that mask data points inconsistent with the criteria. Selection expressions can be combined with graphical, geometric constraints in the retention-time plane as a powerful component for chemical identification with template matching or used to speed and improve mass spectrum library searches.

This paper describes a new technique for removing the background level from digital images produced in comprehensive two-dimensional gas chromatography (GCxGC). Background removal is an important first step in the larger problem of quantitative analysis. The approach estimates the background level across the chromatographic image based on structural and statistical properties of GCxGC data. Then, the background level is subtracted from the image, producing a chromatogram in which the peaks rise above a near-zero mean background. After the background level is removed, further analysis is required to determine the quantitative relationship between the peaks and chemicals in the sample. The algorithm is demonstrated experimentally to be effective at determining and removing the background level from GCxGC images. The algorithm has several parametric controls and is incorporated into an interactive program with graphical interface for rapid and accurate detection of GCxGC peaks.

The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.