Context coding of depth map images under the piecewise-constant image model representation.

This paper introduces an efficient method for lossless compression of depth map images, using the representation of a depth image in terms of three entities: 1) the crack-edges; 2) the constant depth regions enclosed by them; and 3) the depth value over each region. The starting representation is identical with that used in a very efficient coder for palette images, the piecewise-constant image model coding, but the techniques used for coding the elements of the representation are more advanced and especially suitable for the type of redundancy present in depth images. Initially, the vertical and horizontal crack-edges separating the constant depth regions are transmitted by 2D context coding using optimally pruned context trees. Both the encoder and decoder can reconstruct the regions of constant depth from the transmitted crack-edge image. The depth value in a given region is encoded using the depth values of the neighboring regions already encoded, exploiting the natural smoothness of the depth variation, and the mutual exclusiveness of the values in neighboring regions. The encoding method is suitable for lossless compression of depth images, obtaining compression of about 10-65 times, and additionally can be used as the entropy coding stage for lossy depth compression.

Obituary: professor paul dan cristea.

Paul Dan Cristea, professor of Electrical Engineering and Computer Science at 'Politehnica' University of Bucharest died on 17 April 2013, following several years of bravely battling a perfidious illness.

Sparse ptychographical coherent diffractive imaging from noisy measurements.

Ptychography is a lensless coherent diffractive imaging that uses intensity measurements of multiple diffraction patterns collected with a localized illumination probe from overlapping regions of an object. An iterative algorithm is proposed that is targeted on optimal processing noisy measurements. The noise suppression is enabled by two instruments: first, the maximum-likelihood technique formulated for Poissonian (photon-counting) measurements, and, second, sparse approximation of the phase and magnitude of the object and probe. It is shown that the maximum-likelihood estimate of the wavefield at the sensor plane for noisy measurements is essentially different from the famous Gerchberg-Saxton-Fienup solution, where the magnitude of the estimate is replaced by the square root of the intensity measurement. The simulation experiments demonstrate the state-of-the-art performance of the proposed algorithm both numerically and visually.

Compressive sensing computational ghost imaging.

The computational ghost imaging with a phase spatial light modulator (SLM) for wave field coding is considered. A transmission-mask amplitude object is reconstructed from multiple intensity observations. Compressive techniques are used in order to gain a successful image reconstruction with a number of observations (measurement experiments), which is smaller than the image size. Maximum likelihood style algorithms are developed, respectively, for Poissonian and approximate Gaussian modeling of random observations. A sparse and overcomplete modeling of the object enables the advanced high accuracy and sharp imaging. Numerical experiments demonstrate that an approximative Gaussian distribution with an invariant variance results in the algorithm that is efficient for Poissonian observations.

High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude.

We apply a nonlocal adaptive spectral transform for sparse modeling of phase and amplitude of a coherent wave field. The reconstruction of this wave field from complex-valued Gaussian noisy observations is considered. The problem is formulated as a multiobjective constrained optimization. The developed iterative algorithm decouples the inversion of the forward propagation operator and the filtering of phase and amplitude of the wave field. It is demonstrated by simulations that the performance of the algorithm, both visually and numerically, is the current state of the art.

Phase retrieval via spatial light modulator phase modulation in 4f optical setup: numerical inverse imaging with sparse regularization for phase and amplitude.

The 4f optical setup is considered with a wave field modulation by a spatial light modulator located in the focal plane of the first lens. Phase as well as amplitude of the wave field are reconstructed from noisy multiple-intensity observations. The reconstruction is optimal due to a constrained maximum likelihood formulation of the problem. The proposed algorithm is iterative with decoupling of the inverse of the forward propagation of the wave field and the filtering of phase and amplitude. The sparse modeling of phase and amplitude enables the advanced high-accuracy filtering and sharp imaging of the complex-valued wave field. Artifacts typical for the conventional algorithms (wiggles, ringing, waves, etc.) and attributed to optical diffraction can be suppressed by the proposed algorithm.

Wave field reconstruction from multiple plane intensity-only data: augmented lagrangian algorithm.

A complex-valued wave field is reconstructed from intensity-only measurements given at multiple observation planes parallel to the object plane. The phase-retrieval algorithm is obtained from the constrained maximum likelihood approach provided that the additive noise is gaussian. The forward propagation from the object plane to the measurement plane is treated as a constraint in the proposed variational setting of reconstruction. The developed iterative algorithm is based on an augmented lagrangian technique. An advanced performance of the algorithm is demonstrated by numerical simulations.

Backward discrete wave field propagation modeling as an inverse problem: toward perfect reconstruction of wave field distributions.

We consider reconstruction of a wave field distribution in an input/object plane from data in an output/diffraction (sensor) plane. We provide digital modeling both for the forward and backward wave field propagation. A novel algebraic matrix form of the discrete diffraction transform (DDT) originated in Katkovnik et al. [Appl. Opt. 47, 3481 (2008)] is proposed for the forward modeling that is aliasing free and precise for pixelwise invariant object and sensor plane distributions. This "matrix DDT" is a base for formalization of the object wave field reconstruction (backward propagation) as an inverse problem. The transfer matrices of the matrix DDT are used for calculations as well as for the analysis of conditions when the perfect reconstruction of the object wave field distribution is possible. We show by simulation that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms.

Comparison of Affymetrix data normalization methods using 6,926 experiments across five array generations.

BACKGROUND: Gene expression microarray technologies are widely used across most areas of biological and medical research. Comparing and integrating microarray data from different experiments would be very useful, but is currently very challenging due to the experimental and hybridization conditions, as well as data preprocessing and normalization methods. Furthermore, even in the case of the widely-used, industry-standard Affymetrix oligonucleotide microarrays, the various array generations have different probe sets representing different genes, hindering the data integration. RESULTS: In this study our objective is to find systematic approaches to normalize the data emerging from different Affymetrix array generations and from different laboratories. We compare and assess the accuracy of five normalization methods for Affymetrix gene expression data using 6,926 Affymetrix experiments from five array generations. The methods that we compare include 1) standardization, 2) housekeeping gene based normalization, 3) equalized quantile normalization, 4) Weibull distribution based normalization and 5) array generation based gene centering. Our results indicate that the best results are achieved when the data is normalized first within a sample and then between-samples with Array Generation based gene Centering (AGC) normalization. CONCLUSION: We conclude that with the AGC method integrating different Affymetrix datasets results in values that are significantly more comparable across the array generations than in the cases where no array generation based normalization is used. The AGC method was found to be the best method for normalizing the data from several different array generations, and achieve comparable gene values across thousands of samples.

Advanced analysis and visualization of gene copy number and expression data.

BACKGROUND: Gene copy number and gene expression values play important roles in cancer initiation and progression. Both can be measured with high-throughput microarrays and some methodologies to integrate and analyze these data exist. However, varying gene sets within different gene expression and copy number microarrays present significant challenges. RESULTS: We report an advanced version of earlier published CGH-Plotter that rapidly can identify amplified and deleted areas using gene copy number data. With CGH-Plotter v2, the copy number values can be filtered based on the genomic location in basepair units. After filtering, the values for the missing genes can be interpolated. Moreover, the effect of non-informative areas in the genome can be systematically removed by smoothing and interpolating. Further, we developed a tool (ECN) to illustrate the CGH-data values annotated based on the gene expression. The ECN-tool is a MATLAB toolbox enabling straightforward illustration of copy numbers annotated based on the gene expression levels. CONCLUSION: CGH-Plotter v2 provides two methods for analyzing copy number data; dynamic programming and genomic location based smoothing. With ECN-tool the data analyzed with CGH-Plotter v2 can easily be illustrated along the chromosomes individually or along the whole genome. ECN-tool plots the copy number data annotated based on the gene expression data, and it is easy to find the genes that are both over-expressed and amplified or under-expressed and deleted in the samples. From the resulting figures it is straightforward to select interesting genes.

Absolute phase estimation: adaptive local denoising and global unwrapping.

The paper attacks absolute phase estimation with a two-step approach: the first step applies an adaptive local denoising scheme to the modulo-2 pi noisy phase; the second step applies a robust phase unwrapping algorithm to the denoised modulo-2 pi phase obtained in the first step. The adaptive local modulo-2 pi phase denoising is a new algorithm based on local polynomial approximations. The zero-order and the first-order approximations of the phase are calculated in sliding windows of varying size. The zero-order approximation is used for pointwise adaptive window size selection, whereas the first-order approximation is used to filter the phase in the obtained windows. For phase unwrapping, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [IEEE Trans. Image Process.16, 698 (2007)] to the denoised wrapped phase. Simulations give evidence that the proposed algorithm yields state-of-the-art performance, enabling strong noise attenuation while preserving image details.

Systematic bioinformatic analysis of expression levels of 17,330 human genes across 9,783 samples from 175 types of healthy and pathological tissues.

Our knowledge on tissue- and disease-specific functions of human genes is rather limited and highly context-specific. Here, we have developed a method for the comparison of mRNA expression levels of most human genes across 9,783 Affymetrix gene expression array experiments representing 43 normal human tissue types, 68 cancer types, and 64 other diseases. This database of gene expression patterns in normal human tissues and pathological conditions covers 113 million datapoints and is available from the GeneSapiens website.

Discrete diffraction transform for propagation, reconstruction, and design of wavefield distributions.

A discrete diffraction transform (DDT) is a novel discrete wavefield propagation model that is aliasing free for a pixelwise invariant object distribution. For this class of distribution, the model is precise and has no typical discretization effects because it corresponds to accurate calculation of the diffraction integral. A spatial light modulator (SLM) is a good example of a system where a pixelwise invariant distribution appears. Frequency domain regularized inverse algorithms are developed for reconstruction of the object wavefield distribution from the distribution given in the sensor plane. The efficiency of developed frequency domain algorithms is demonstrated by simulation.

Phase local approximation (PhaseLa) technique for phase unwrap from noisy data.

The local polynomial approximation (LPA) is a nonparametric regression technique with pointwise estimation in a sliding window. We apply the LPA of the argument of cos and sin in order to estimate the absolute phase from noisy wrapped phase data. Using the intersection of confidence interval (HCI) algorithm, the window size is selected as adaptive pointwise varying. This adaptation gives the phase estimate with the accuracy close to optimal in the mean squared sense. For calculations, we use a Gauss-Newton recursive procedure initiated by the phase estimates obtained for the neighboring points. It enables tracking properties of the algorithm and its ability to go beyond the principal interval [-pi, pi] and to reconstruct the absolute phase from wrapped phase observations even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for noisy phase unwrap. The theoretical analysis produced for the accuracy of the pointwise estimates is used for justification of the HCI adaptation algorithm.

Blur identification by multilayer neural network based on multivalued neurons.

A multilayer neural network based on multivalued neurons (MLMVN) is a neural network with a traditional feedforward architecture. At the same time, this network has a number of specific different features. Its backpropagation learning algorithm is derivative-free. The functionality of MLMVN is superior to that of the traditional feedforward neural networks and of a variety kernel-based networks. Its higher flexibility and faster adaptation to the target mapping enables to model complex problems using simpler networks. In this paper, the MLMVN is used to identify both type and parameters of the point spread function, whose precise identification is of crucial importance for the image deblurring. The simulation results show the high efficiency of the proposed approach. It is confirmed that the MLMVN is a powerful tool for solving classification problems, especially multiclass ones.

Inference of gene regulatory networks based on a universal minimum description length.

The Boolean network paradigm is a simple and effective way to interpret genomic systems, but discovering the structure of these networks remains a difficult task. The minimum description length (MDL) principle has already been used for inferring genetic regulatory networks from time-series expression data and has proven useful for recovering the directed connections in Boolean networks. However, the existing method uses an ad hoc measure of description length that necessitates a tuning parameter for artificially balancing the model and error costs and, as a result, directly conflicts with the MDL principle's implied universality. In order to surpass this difficulty, we propose a novel MDL-based method in which the description length is a theoretical measure derived from a universal normalized maximum likelihood model. The search space is reduced by applying an implementable analogue of Kolmogorov's structure function. The performance of the proposed method is demonstrated on random synthetic networks, for which it is shown to improve upon previously published network inference algorithms with respect to both speed and accuracy. Finally, it is applied to time-series Drosophila gene expression measurements.

Jointly analyzing gene expression and copy number data in breast cancer using data reduction models.

With the growing surge of biological measurements, the problem of integrating and analyzing different types of genomic measurements has become an immediate challenge for elucidating events at the molecular level. In order to address the problem of integrating different data types, we present a framework that locates variation patterns in two biological inputs based on the generalized singular value decomposition (GSVD). In this work, we jointly examine gene expression and copy number data and iteratively project the data on different decomposition directions defined by the projection angle theta in the GSVD. With the proper choice of theta, we locate similar and dissimilar patterns of variation between both data types. We discuss the properties of our algorithm using simulated data and conduct a case study with biologically verified results. Ultimately, we demonstrate the efficacy of our method on two genome-wide breast cancer studies to identify genes with large variation in expression and copy number across numerous cell line and tumor samples. Our method identifies genes that are statistically significant in both input measurements. The proposed method is useful for a wide variety of joint copy number and expression-based studies. Supplementary information is available online, including software implementations and experimental data.

A spatially adaptive nonparametric regression image deblurring.

We propose a novel nonparametric regression metthod for deblurring noisy images. The method is based on the local polynomial approximation (LPA) of the image and the paradigm of intersecting confidence intervals (ICI) that is applied to define the adaptive varying scales (window sizes) of the LPA estimators. The LPA-ICI algorithm is nonlinear and spatially adaptive with respect to smoothness and irregularities of the image corrupted by additive noise. Multiresolution wavelet algorithms produce estimates which are combined from different scale projections. In contrast to them, the proposed ICI algorithm gives a varying scale adaptive estimate defining a single best scale for each pixel. In the new algorithm, the actual filtering is performed in signal domain while frequency domain Fourier transform operations are applied only for calculation of convolutions. The regularized inverse and Wiener inverse filters serve as deblurring operators used jointly with the LPA-design directional kernel filters. Experiments demonstrate the state-of-art performance of the new estimators which visually and quantitatively outperform some of the best existing methods.

Gene-expression profiling predicts recurrence in Dukes' C colorectal cancer.

BACKGROUND & AIMS: Although approximately 50% of Dukes' C colorectal cancer patients are surgically cured, it is currently not possible to distinguish these patients from those at high risk of recurrence. The recent advent of routine adjuvant chemotherapy for these patients has greatly complicated the identification of new markers predicting the response to surgery, which is now reliant on archived materials. Microarray analysis allows fine tumor classification but cannot be used with paraffin-embedded archival samples. METHODS: We used microarray analysis of a unique set of fresh-frozen tumor samples from Dukes' C patients who had surgery as the only form of treatment to identify molecular signatures that characterize tumors from patients with good and bad prognosis. RESULTS: Unsupervised hierarchical clustering and a K-nearest neighbors-based classifier identified groups of patients with significantly different survival (P = .019 and P = .0001). Expression profiling outperformed previously reported genetic markers of prognosis such as TP53 and K-RAS mutational status and allelic imbalance in chromosome 18q, which were of limited prognostic power in this study. Functional categories significantly enriched in gene-expression differences included protein transport and folding. The prognostic potential of the RAS homologue RHOA, one of the most differentially expressed genes, was further investigated using immunohistochemistry and a tissue microarray containing 137 independent Dukes' C tumor samples. Reduced RHOA expression was associated with significantly shorter survival (P = .01). CONCLUSIONS: This study shows that gene-expression profiling of surgical tumor samples can predict recurrence in Dukes' C patients. Therefore, this approach could be used to guide decisions concerning the clinical management of these patients.