2D Signals Research Articles

Coherence Quantum Beats in Two-Dimensional Electronic Spectroscopy

We study the coherence quantum beats in two-dimensional (2D) electronic spectroscopy of a coupled dimer system using a theoretical method based on a time-nonlocal quantum master equation and a recently proposed scheme for the evaluation of the third-order photon echo polarization [Gelin, M. F.; Egorova, D.; Domcek, W. J. Chem. Phys. 2005, 123, 164112]. The simulations show that the amplitude and peak shape beating in the 2D spectra is a result of the interplay between the rephasing and non-rephasing contributions to the 2D signals and can be used to elucidate the coherence dynamics in a multichromophoric system. In addition, the results suggest that the rephasing and non-rephasing 2D spectra contain complementary information, and a study of both of them could provide more dynamical information from 2D electronic spectroscopy.

Hardware Implementation of a Spline-Based Genetic Algorithm for Embedded Stereo Vision Sensor Providing Real-Time Visual Guidance to the Visually Impaired

Many image and signal processing techniques have been applied to medical and health care applications in recent years. In this paper, we present a robust signal processing approach that can be used to solve the correspondence problem for an embedded stereo vision sensor to provide real-time visual guidance to the visually impaired. This approach is based on our new one-dimensional (1D) spline-based genetic algorithm to match signals. The algorithm processes image data lines as 1D signals to generate a dense disparity map, from which 3D information can be extracted. With recent advances in electronics technology, this 1D signal matching technique can be implemented and executed in parallel in hardware such as field-programmable gate arrays (FPGAs) to provide real-time feedback about the environment to the user. In order to complement (not replace) traditional aids for the visually impaired such as canes and Eyes dogs, vision systems that provide guidance to the visually impaired must be affordable, easy to use, compact, and free from attributes that are awkward or embarrassing to the user. Seeing Eye Glasses, an embedded stereo vision system utilizing our new algorithm, meets all these requirements.

Dynamics of distributed 1D and 2D motion representations for short-latency ocular following

Integrating information is essential to measure the physical 2D motion of a surface from both ambiguous local 1D motion of its elongated edges and non-ambiguous 2D motion of its features such as corners or texture elements. The dynamics of this motion integration shows a complex time course as read from tracking eye movements: first, local 1D motion signals are extracted and pooled to initiate ocular responses, then 2D motion signals are integrated to adjust the tracking direction until it matches the surface motion direction. The nature of these 1D and 2D motion computations are still unclear. One hypothesis is that their different dynamics may be explained from different contrast sensitivities. To test this, we measured contrast–response functions of early, 1D-driven and late, 2D-driven components of ocular following responses to different motion stimuli: gratings, plaids and barberpoles. We found that contrast dynamics of 1D-driven responses are nearly identical across the different stimuli. On the contrary, late 2D-driven components with either plaids or barberpoles have similar latencies but different contrast dynamics. Temporal dynamics of both 1D- and 2D-driven responses demonstrates that the different contrast gains are set very early during the response time course. Running a Bayesian model of motion integration, we show that a large family of contrast–response functions can be predicted from the probability distributions of 1D and 2D motion signals for each stimulus and by the shape of the prior distribution. However, the pure delay (i.e. largely independent upon contrast) observed between 1D- and 2D-motion supports the fact that 1D and 2D probability distributions are computed independently. This two-pathway Bayesian model supports the idea that 1D and 2D mechanisms represent edges and features motion in parallel.

Linear and nonlinear methods of 2D signal processing during automated ultrasonic testing

Problems of signal preprocessing as applied to automated ultrasonic testing are considered. Methods for signal processing in the spatial and frequency domains are presented.

Sigma–delta cellular neural network for 2D modulation

Although sigma-delta modulation is widely used for analog-to-digital (A/D) converters, sigma-delta concepts are only for 1D signals. Signal processing in the digital domain is extremely useful for 2D signals such as used in image processing, medical imaging, ultrasound imaging, and so on. The intricate task that provides true 2D sigma-delta modulation is feasible in the spatial domain sigma-delta modulation using the discrete-time cellular neural network (DT-CNN) with a C-template. In the proposed architecture, the A-template is used for a digital-to-analog converter (DAC), the C-template works as an integrator, and the nonlinear output function is used for the bilevel output. In addition, due to the cellular neural network (CNN) characteristics, each pixel of an image corresponds to a cell of a CNN, and each cell is connected spatially by the A-template. Therefore, the proposed system can be thought of as a very large-scale and super-parallel sigma-delta modulator. Moreover, the spatio-temporal dynamics is designed to obtain an optimal reconstruction signal. The experimental results show the excellent reconstruction performance and capabilities of the CNN as a sigma-delta modulator.

A new approach to the spatio-temporal pattern identification in neuronal multi-electrode registrations

A lot of methods were created in last decade for the spatio-temporal analysis of multi-electrode array (MEA) neuronal data sets. All these methods were implemented starting from a channel to channel analysis, with a great computational effort and onerous spatial pattern recognition task. Our idea is to approach the MEA data collection from a different point of view, i.e. considering all channels simultaneously. We transform the 2D plus time MEA signal in a mono-dimensional plus time signal and elaborate it as a normal 1D signal, using the Space-Amplitude Transform method. This geometrical transformation is completely invertible and allows to employ very fast processing algorithms.

A new approach to the spatio-temporal pattern identification in neuronal multi-electrode registrations

AbstractA lot of methods were created in last decade for the spatio-temporal analysis of multi-electrode array (MEA) neuronal data sets. All these methods were implemented starting from a channel to channel analysis, with a great computational effort and onerous spatial pattern recognition task. Our idea is to approach the MEA data collection from a different point of view, i.e. considering all channels simultaneously. We transform the 2D plus time MEA signal in a mono-dimensional plus time signal and elaborate it as a normal 1D signal, using the Space-Amplitude Transform method. This geometrical transformation is completely invertible and allows to employ very fast processing algorithms.

CONTOUR-BASED FEATURE EXTRACTION USING DUAL-TREE COMPLEX WAVELETS

A contour-based feature extraction method is proposed by using the dual-tree complex wavelet transform and the Fourier transform. Features are extracted from the 1D signals r and θ, and hence the processing memory and time are reduced. The approximate shift-invariant property of the dual-tree complex wavelet transform and the Fourier transform guarantee that this method is invariant to translation, rotation and scaling. The method is used to recognize aircrafts from different rotation angles and scaling factors. Experimental results show that it achieves better recognition rates than that which uses only the Fourier features and Granlund's method. Its success is due to the desirable shift invariant property of the dual-tree complex wavelet transform, the translation invariant property of the Fourier spectrum, and our new complete representation of the outer contour of the pattern.

POSITION-DEPENDENT LAGRANGE INTERPOLATING MULTIRESOLUTIONS

This paper is devoted to the construction of interpolating multiresolutions using Lagrange polynomials and incorporating a position dependency. It uses the Harten's framework21 and its connection to subdivision schemes. Convergence is first emphasized. Then, plugging the various ingredients into the wavelet multiresolution analysis machinery, the construction leads to position-dependent interpolating bases and multi-scale decompositions that are useful in many instances where classical translation-invariant frameworks fail. A multivariate generalization is proposed and analyzed. We investigate applications to the reduction of the so-called Gibbs phenomenon for the approximation of locally discontinuous functions and to the improvement of the compression of locally discontinuous 1D signals. Some applications to image decomposition are finally presented.

Quaternion Fourier Descriptors for the Preprocessing and Recognition of Spoken Words Using Images of Spatiotemporal Representations

This paper presents an application of the quaternion Fourier transform for the preprocessing for neural-computing. In a new way the 1D acoustic signals of French spoken words are represented as 2D signals in the frequency and time domain. These kind of images are then convolved in the quaternion Fourier domain with a quaternion Gabor filter for the extraction of features. This approach allows to greatly reduce the dimension of the feature vector. Two methods of feature extraction are tested. The features vectors were used for the training of a simple MLP, a TDNN and a system of neural experts. The improvement in the classification rate of the neural network classifiers are very encouraging which amply justify the preprocessing in the quaternion frequency domain. This work also suggests the application of the quaternion Fourier transform for other image processing tasks.

FPGA Implementation of 2D Signals Encoder Using QMF Based Dyadic DWT: Application to Neutron Tomography Projections

FPGA Implementation of 2D Signals Encoder Using QMF Based Dyadic DWT: Application to Neutron Tomography Projections

Two-dimensional FIR signal adapted filter banks: Optimality and design

The effect of different subsampling matrices with the same sampling density, on the optimality of two-dimensional filter banks is studied in this paper. It is seen that, in the case of two channel filter banks, there can be three distinct filter banks for an input power spectral density, with each one optimum for the corresponding subsampling matrix. For most of the natural images, the quincunx filter bank is optimum. In addition to this, a suboptimal solution that extends one-dimensional (1D) signal adapted filter bank design procedure, to two-dimensional (2D) nonseparable and separable signal adapted filter banks, using iterative greedy algorithm, is proposed. The nonseparable filter bank is designed for both four channel and two channel quincunx filter banks. A cascade structure is used for the factorization of 2D paraunitary polyphase matrix in the nonseparable case and a 2D separable FIR PU polyphase matrix is used in the separable case. The simulated FIR responses match the ideal responses very closely.

Wavelet based multi-spectral image analysis of maize leaf chlorophyll content

With recent advancement in precision farming, the need for variable rate technology has become apparent. Variable rate technology can improve the efficiency of farm operations and lessen farm's environmental impact. To implement effective variable rate applications, it is essential to gather and process information on crop nitrogen level reliably. This research is intended to develop an image-processing method to assess crop nitrogen level based on multi-spectral images of maize plants. This method first removed unnecessary information from the image and then converted the image into a one-dimensional (1D) signal representing the reflectance of the maize plant across leaves. The obtained data was further processed using the wavelet packet transform to find specific patterns that correspond to crop nitrogen stress. To implement wavelet analysis, the 1D signal was deconstructed into packets of narrow frequency bands to find the lowest level approximations at different levels. The maximum wavelet coefficients were identified for interested signal bands and then compared to SPAD meter readings, which were used as the ground-truth corn nitrogen level. Analysis results indicated that the db4 wavelet at a level 8 deconstruction had the highest linear regression coefficient ( R 2 = 0.78) with a high correlation coefficient ( r = 0.88) for corn nitrogen levels.

Equilibrium and dissipative structures role on images

This paper introduces entropy as a feature for 1D signals. We propose as entropy measure the ratio between the signal’s perturbation (i.e. its part within minimum and maximum grey level) and the total energy of the signal. A linear transformation of 2D signals into 1D signals is also illustrated together with the results concerning natural scene, texture and medical images from a large mammograms database. The aim of this paper is to verify if the entropy variations for a closed system can be a discriminant feature to select homogenous regions.

Parity symmetry in multi-dimensional signals

Parity symmetry is an important local feature for qualitative signal analysis. It is strongly related to the local phase of the signal. In image processing parity symmetry is a cue for the line-like or edge-like quality of a local image structure. The analytic signal is a well-known representation for 1D signals, which enables the extraction of local spectral representations as amplitude and phase. Its representation domain is that of the complex numbers. We will give an overview how the analytic signal can be generalized to the monogenic signal in the $n$D case within a Clifford valued domain. The approach is based on the Riesz transform as a generalization of the Hilbert transform with respect to the embedding dimension of the structure. So far we realized the extension to 2D and 3D signals. We learned to take advantage of interesting effects of the proposed generalization as the simultaneous estimation of the local amplitude, phase and orientation, and of image analysis in the monogenic scale-space.

Finite Discrete, Shift-Invariant, Directional Filterbanks for Visual Information Processing, I : Construction

As is well known in neuroscience, simple cells of the mammalian’s striate cortex possess both orientation and spatial-frequency selectivity, and are similar to the Gabor filters or Gaussian derivative filters in shape. The purpose of this paper is to propose a method of designing perfect reconstruction 2D filterbanks which act on finite dimensional linear spaces consisting of 2D signals of a certain size, and have several analogous features to simple cells: (1) the filterbanks consist of several spatial-frequency channels with orientation selectivity, (2) the filterbanks have shift-invariant multiresolution (multiscale) structures, (3) filters contained in them are FIR, and are similar in appearance to not only Gaussian derivatives of 1st and 2nd order, but also ones of higher order. Moreover, they are constructed by finite linear combinations of separable filters. As is described in the text, by virtue of these properties, our 2D filterbanks can become bases of constructing computational nonlinear models of visual information processing. In this paper we construct the 2D filterbanks, and discuss them from the viewpoint of vision science. For example we disclose a possible role of “Gaussian-derivative-like” filters of higher order in our filterbanks. Practical applications of our 2D filterbanks to vision science and image processing will be given in our subsequent papers.

Variety of stylolites morphologies and statistical characterization of the amount of heterogeneities in the rock

The surface roughness of several stylolites in limestones was measured using high-resolution laser profilometry. The 1D signals obtained were statistically analyzed to determine the scaling behavior and calculate a roughness exponent, also called Hurst exponent. Statistical methods based on the characterization of a single Hurst exponent imply strong assumptions on the mathematical characteristics of the signal: the derivative of the signal (or local increments) should be stationary and has finite variance. The analysis of the measured stylolites shows that these properties are not always verified simultaneously. The stylolite profiles show persistence and jumps and several stylolites are not regular, with alternating regular and irregular portions. A new statistical method is proposed here, based on a non-stationary but Gaussian model, to estimate the roughness of the profiles and quantify the heterogeneity of stylolites. This statistical method is based on two parameters: the local roughness (H ), which describes the local amplitude of the stylolite, and the amount of irregularities on the signal (m), which can be linked to the heterogeneities initially present in the rock before the stylolite formed. Using this technique, a classification of the stylolites in two families is proposed: those for which the morphology is homogeneous everywhere and those with alternating regular and irregular portions. � 2006 Elsevier Ltd. All rights reserved.

Variety of stylolites' morphologies and statistical characterization of the amount of heterogeneities in the rock

The surface roughness of several stylolites in limestones was measured using high-resolution laser profilometry. The 1D signals obtained were statistically analyzed to determine the scaling behavior and calculate a roughness exponent, also called Hurst exponent. Statistical methods based on the characterization of a single Hurst exponent imply strong assumptions on the mathematical characteristics of the signal: the derivative of the signal (or local increments) should be stationary and has finite variance. The analysis of the measured stylolites shows that these properties are not always verified simultaneously. The stylolite profiles show persistence and jumps and several stylolites are not regular, with alternating regular and irregular portions. A new statistical method is proposed here, based on a non-stationary but Gaussian model, to estimate the roughness of the profiles and quantify the heterogeneity of stylolites. This statistical method is based on two parameters: the local roughness ( H), which describes the local amplitude of the stylolite, and the amount of irregularities on the signal ( μ), which can be linked to the heterogeneities initially present in the rock before the stylolite formed. Using this technique, a classification of the stylolites in two families is proposed: those for which the morphology is homogeneous everywhere and those with alternating regular and irregular portions.

Advantages of the Hilbert Huang transform for marine mammals signals analysis

While marine mammals emit variant signals (in time and frequency), the Fourier spectrogram appears to be the most widely used spectral estimator. In certain cases, this approach is suboptimal, particularly for odontocete click analysis and when the signal-to-noise ratio varies during the continuous recordings. We introduce the Hilbert Huang transform (HHT) as an efficient means for analysis of bioacoustical signals. To evaluate this method, we compare results obtained from three time-frequency representations: the Fourier spectrogram, the wavelet transform, and the Hilbert Huang transform. The results show that HHT is a viable alternative to the wavelet transform. The chosen examples illustrate certain advantages. (1) This method requires the calculation of the Hilbert transform; the time-frequency resolution is not restricted by the uncertainty principle; the frequency resolution is finer than with the Fourier spectrogram. (2) The original signal decomposition into successive modes is complete. If we were to multiply some of these modes, this would contribute to attenuate the presence of noise in the original signal and to being able to select pertinent information. (3) Frequency evolution for each mode can be analyzed as one-dimensional (1D) signal. We not need a complex 2D post-treatment as is usually required for feature extraction.

Polarization encoding and multiplexing of two-dimensional signals: application to image encryption

We discuss an optical system that encodes an input signal to a polarization state, using a spatial light modulator (SLM). Using two SLMs the optical system multiplexes two 2D signals in the polarization domain, and we demonstrate the multiplexing of two binary images. The encryption and decryption of two binary images using an XOR operation is also presented.