Anh Phuong Tran

An efficient pyramid image coding system

The pyramid image structure can be naturally adapted for progressive image transmission over low-speed channels and hierarchical image retrieving in computerized image archiving. An efficient pyramid image coding system using quadrature mirror filters to form the image-pyramids is proposed in this paper. Characteristics of the image-pyramids are presented. Since the Laplacian pyramids of most nature images contain sparse and spatially concentrated data, a combined run-length coding for zero-valued elements and entropy coding for elements larger than a certain threshold is employed. The textural features in the Laplacian pyramids suggest that coding techniques pursuing spatial correlation may be advantageous. Therefore, vector quantization is chosen to code the Laplacian pyramids. Simulation results have shown that simple vector quantization accomplished significant bit-rate reduction over scalar quantization. The proposed system has also shown good-quality reproduction at bit rates lower than 1 bit/pixel.

Near-field or far-field full-wave ground penetrating radar modeling as a function of the antenna height above a planar layered medium

The selection of a near-field or far-field ground-penetrating radar (GPR) model is an important question for an accurate but computationally effective characterization of medium electrical properties using full-wave inverse modeling. In this study, we determined an antenna height threshold for the near-field and far-field full-wave GPR models by analyzing the variation of the spatial derivatives of the Greens function over the antenna aperture. The obtained results show that the ratio of this threshold to the maximum dimension of the antenna aperture is approximately equal to 1.2. Subsequently, we validated the finding threshold through numerical and laboratory experiments using a homemade 1-3 GHz Vivaldi antenna with an aperture of 24 cm. For the numerical experiments, we compared the synthetic GPR data generated from several scenarios of layered medium using both near-field and far-field antenna models. The results showed that above the antenna height threshold, the near-field and far-field GPR data perfectly agree. For the laboratory experiments, we conducted GPR measurements at different antenna heights above a water layer. The near-field model performed better for antenna heights smaller than the threshold value (± 29 cm), while both models provided similar results for larger heights. The results obtained by this study provides valuable insights to specify the antenna height threshold above which the far-field model can be used for a given antenna.

Validation of Near-Field Ground-Penetrating Radar Modeling Using Full-Wave Inversion for Soil Moisture Estimation

We present validation results of a new ground-penetrating radar (GPR) near-field model for determining the electrical properties and correlated water content of a sand using both frequency- and time-domain radars. The radar antennas are intrinsically characterized using an equivalent set of infinitesimal source/field points and characteristic functions of antennas, which were determined using measurements with the antenna at different distances from a copper plane. The antenna radiation was modeled using six source and field points, which was found to be a good compromise between high modeling accuracy and computing efficiency. We validated our model by inverting GPR data to predict the water content of a sand layer subject to seven levels of saturation. A soil dielectric mixing model was integrated into the full-wave GPR inverse modeling to directly estimate the water content and to account for the frequency dependence of the electrical properties. Although the quality of the fit slightly decreased as the antenna approached the sand surface, the results showed a close agreement between measured and modeled data, resulting in accurate estimation of the water content. The average errors of all water content estimates were 0.012 cm3/cm3 for the frequency domain and 0.016 cm3/cm3 for the time-domain GPR. However, the accuracy reduced when the sand became wet. By performing numerical simulations, we found that it is due to the vertical heterogeneity of soil moisture under the effect of the hydrostatic pressure. We also showed that the GPR inversion with the multilayered soil model could account for this heterogeneity and improved the agreement between the modeled and measured GPR data as well as the accuracy of soil moisture estimation. As for the frequency dependence of the electrical properties, in the frequency ranges of both GPR systems, while the dielectric permittivity was approximately constant, the apparent conductivity exponentially increased with increasing frequency. The success of the calibration and validation in laboratory conditions demonstrates a great potential for practical applications of the radar model, notably for the digital soil mapping and nondestructive testing of materials.

Minimization of multiple-output exclusive-OR switching functions

A method to minimize Reed-Muller polynomials in mixed polarity for multiple-output functions is presented. The multiple outputs are first minimized as single-output functions. Each of the multiple outputs is further minimized according to a predetermined order, one at a time. Minimization of an output is carried out by trying to make the best use of existing product terms in previously minimized outputs. The minimization algorithm is implemented by a computer program.

Near-field modeling of radar antennas for wave propagation in layered media: When models represent reality

Characterization of the electrical properties of a medium using ground-penetrating radar (GPR) appeals to inverse modeling, which has remained a major challenge in applied geophysics in particular due to antenna modeling limitations. In this paper, we propose a new near-field radar modeling approach for wave propagation in layered media. Radar antennas are modeled using an equivalent set of infinitesimal electric dipoles and characteristic, frequency-dependent, global reflection and transmission coefficients. These coefficients determine, through a plane wave decomposition, wave propagation between the radar reference plane, point sources, and field points. The interactions between the antenna and the medium are thereby inherently accounted for. The fields are calculated using three-dimensional Greens functions. We validated the model using both time and frequency domain radars. The antennas were calibrated using measurements at different heights above a copper plane. The proposed model provided unprecedented results for describing near-field radar data collected over water, whose frequency-dependent electrical properties were described using the Debye model. Very good agreements were also obtained for measurements collected over water as validating medium for the inversions. The proposed modeling approach is fast and shows great promise for digital soil mapping or non-destructive material characterization.

Soil moisture estimation using full-wave inversion of near- and far-field ground-penetrating radar data: A comparative evaluation

A new near-field ground-penetrating antenna model was applied for characterization of soil moisture in an agricultural transect in central Belgium. The measurement system consists of a vector network analyzer connected with a horn antenna and a differential GPS mounted on a motorcycle for quick data acquisition. Numerical experiments show that near-field GPR data are more sensitive to the soil dielectric properties than far-field data due to nearer distance between the antenna and medium. For the field measurements, the modeled GPR data from far-field and near-field configurations agree very well with the measured ones. However, soil water content estimated from near-field data is higher and more in agreement with Theta Probe measurements than far-field owning to the deeper penetration depth, smaller foot print and larger sensitivity with soil permittivity of near-field data. The results also show that the spatial pattern of the soil moisture is mainly controlled by the topography, while temporal variability is influenced by the rainfall intensity and time lag between rainfall event and experiment. The proposed approach shows a promising potential for temporal and spatial characterization of soil moisture at the field scale.

Intrinsic modeling of antenna array in near-field conditions

Antenna arrays have been increasingly used in many civil engineering and geoscience applications as they allow collecting multi-offset measurements simultaneously, thereby providing additional information for subsurface imaging and characterization. We extended a new near-field intrinsic antenna modeling approach to antenna arrays. The array was considered as a combination of couples of transmitting-receiving antennas with different offsets. Each couple of antennas was characterized using an equivalent set of infinitesimal source/field points and reflection/transmission transfer functions. We proposed an iterative approach to calibrate the model through which the antenna model was progressively completed. To reduce the number of simultaneous unknown parameters, linear and nonlinear optimization algorithms were combined together. We also applied the time gain for both modeled and measured array data to compensate for the wave attenuation, which is expected to improve the accuracy of the calibration. We validated the proposed calibration approach to an antenna array with two-Vivaldi antenna elements operating in the frequency range 0.8-3 GHz. The offsets between the two antennas were 20 and 40 cm, respectively. Calibration data consisted of 100 measurements corresponding to the antenna array at 100 different distances from a copper plane. The calibrated and measured antenna array data closely agree, with correlation coefficients larger than 0.9979 and root mean square error less than 2.3×10-5. These results open a new development avenue to apply the antenna array for digital soil mapping and non-destructive testing of materials using full-wave inverse modeling.

Overflow detection in multioperand addition

An algorithm is developed to detect overflow in multioperand addition. The algorithm is extended to support generic commercial arithmetic adder chips. This algorithm is used in conjunction with a multioperand carry-save adder and a multioperand bit-serial adder to detect overflow. Provision is also made in these circuits to incorporate subtraction of operands. CAD tools are used to simulate the logic in hardware for the verification of the algorithm.

Block-Effect Reduction In Transform Coding

With the advancement in computational speed, transform coding has been a promising technique in image data compression. Traditionally, an image is divided into exclusive rectangular blocks or subimages. Each subimage is a partial scene of the original image and they are processed independently. In low-bit rate applications, block boundary can develop due to discontinuities between the subimages. A two-stage transform coding scheme to reduce such effect is proposed. The first stage transformation is applied to the subimages, each being a reduced under-sampled image of the original. The second stage transformation is applied to the transform coefficients obtained at the first stage. A simple coder with discrete Walsh-Hadamard transform and uniform quantization is used to compare the preliminary simulation results obtained from the proposed scheme and the traditional method.

Soil permittivity and conductivity characterization by full-wave inversion of near-field GPR data

Full-wave inverse modeling of low-frequency, near-field ground-penetrating radar (GPR) data was used for simultaneously reconstructing both the electric permittivity and conductivity of the soil. Low GPR frequencies provide a significant sensitivity of the reflection coefficient to electrical conductivity and are less affected by soil roughness and local heterogeneities. Based on the near-field model, several numerical experiments were conducted to simultaneously retrieve ground electrical conductivities and dielectrical permittivities in the range 10-180 MHz for different water contents. We calibrated a time-domain GPR system equipped with transmitting and receiving 80 MHz unshielded dipoles antennas using measurements collected at different heights over a water layer of known electrical conductivity. Then, the GPR model was validated for measurements collected over water subject to a range of electrical conductivities. A good agreement was obtained between the radar data and the fullwave electromagnetic model for the different antenna heights but the water layer properties were not accurately retrieved. These differences were attributed to errors in the transfer functions of the antenna mainly due to the instability of the radar system. The future challenge in this research will focus on an accurate determination of the antenna transfer functions of a stable radar system for improved medium reconstruction.