Search

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. OCIS codes: 070.2025, 100.3010, 100.3190.

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. OCIS codes: 100.5088, 110.5086, 280.0280.

The problem of predicting a sequence [x.sub.1], [x.sub.2], ... generated by a discrete source with unknown statistics is considered. Each letter [x.sub.t+1] is predicted using the information on the word [x.sub.1][x.sub.2] ... [x.sub.t] only. This problem is of great importance for data compression, because of its use to estimate probability distributions for PPM algorithms and other adaptive codes. On the other hand, such prediction is a classical problem which has received much attention. Its history can be traced back to Laplace. We address the problem where the sequence is generated by an independent and identically distributed (i.i.d.) source with some large (or even infinite) alphabet and suggest a class of new methods of prediction. Index Terms--Adaptive coding, Laplace problem of succession, lossless data compression, prediction of random processes, Shannon entropy, source coding.

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. OCIS codes: 070.2025, 100.3010, 100.3190.

Local polynomial approximation (LPA) technique was used for estimating the absolute phase reconstruction from noisy wrapped phase data. Findings revealed a reasonable compromise between the noise smoothing and preservation of details in phase image due to window size adaptation.

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. Index Terms--Blind deconvolution, complex-valued neuron, derivative-free learning, feedforward network, multivalued neuron.

The idea of generalized Fresnel functions, which traces back to expressing a discrete transform as a linear convolution, is developed. The generalized Fresnel functions for the discrete Fourier transform (DFT) are found, and it is shown that DFT of even order has two generalized Fresnel functions, while DFT of odd order has a single generalized Fresnel function.

A novel nonparametric regression method for deblurring noisy images is proposed. The regularized inverse and Wiener inverse filters serve as deblurring operator used jointly with the local polynomial approximation-design directional kernel filters.

A nonlinear extension of linear filters optimizing under mean-square error criterion the memory function is introduced which is in the core of distributed-arithmetic based implementation. The results indicate improvement in the filtering of noise, which might contain non-Gaussian components without increasing the complexity of implementation.

Abstract 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.

We propose new multistage interconnection networks (MIN) for scalable parallel Viterbi decoder architectures. The architecture consists of the desired number of processing elements (PE) connected by the suggested MINs, thus allowing a tradeoff between the complexity and the speed. The structure of the MIN is derived first by transforming the de Bruijn interconnection-based Viterbi algorithm trellis into the equivalent trellis with a perfect shuffle interconnection, and then applying new decomposition of the perfect shuffle operator. This results in an efficient modular system and data flow is formed by the shuffling in a local PE memory and data exchange through a fixed interconnection between PE. We suggest several solutions for 1/n and k/n rate codes, where k denotes the number of input bits shifting into k shift registers of the encoder. Index Terms--Multistage interconnection networks (MINs), Viterbi algorithm (VA) architecture, Viterbi decoding.