Multidimensional Adaptive Filtering Research Articles

Multidimensional Seismic Data Reconstruction Using Frequency-Domain Adaptive Prediction-Error Filter

Seismic data interpolation and reconstruction play an important role in seismic data processing. Seismic data are often inadequately sampled along various spatial axes. We have developed a new approach to interpolate aliased multidimensional seismic data based on the multidimensional adaptive prediction-error filter in frequency domain. First, we estimate the adaptive prediction-error filter coefficients, then interpolate missing traces using the estimated coefficients. Shaping regularization is used to control the smoothness of frequency-domain multidimensional adaptive prediction-error filter coefficients. Instead of estimating prediction-error filter coefficients only along one direction space, we estimate the prediction-error filter coefficients using more information along different direction spaces. So, multidimensional adaptive prediction-error filter using regularized nonstationary autoregression can adaptively estimate seismic events whose slopes vary in multidimensional space. The frequency-domain multidimensional interpolation method can input data at temporal frequency, which can save computer memory and time. For multidimensional seismic data, which miss different number of traces regularly in different axes, the proposed method can be used to interpolate missing traces to obtain more accurate results. The proposed method improves the calculation efficiency by applying shaping regularization and implementation in the frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.

Fast GPU Based Adaptive Filtering of 4D Echocardiography

Time resolved three-dimensional (3D) echocardiography generates four-dimensional (3D+time) data sets that bring new possibilities in clinical practice. Image quality of four-dimensional (4D) echocardiography is however regarded as poorer compared to conventional echocardiography where time-resolved 2D imaging is used. Advanced image processing filtering methods can be used to achieve image improvements but to the cost of heavy data processing. The recent development of graphics processing unit (GPUs) enables highly parallel general purpose computations, that considerably reduces the computational time of advanced image filtering methods. In this study multidimensional adaptive filtering of 4D echocardiography was performed using GPUs. Filtering was done using multiple kernels implemented in OpenCL (open computing language) working on multiple subsets of the data. Our results show a substantial speed increase of up to 74 times, resulting in a total filtering time less than 30 s on a common desktop. This implies that advanced adaptive image processing can be accomplished in conjunction with a clinical examination. Since the presented GPU processor method scales linearly with the number of processing elements, we expect it to continue scaling with the expected future increases in number of processing elements. This should be contrasted with the increases in data set sizes in the near future following the further improvements in ultrasound probes and measuring devices. It is concluded that GPUs facilitate the use of demanding adaptive image filtering techniques that in turn enhance 4D echocardiographic data sets. The presented general methodology of implementing parallelism using GPUs is also applicable for other medical modalities that generate multidimensional data.

Predicting respiratory tumor motion with multi-dimensional adaptive filters and support vector regression**Portions of this work were presented as an oral presentation at ASTRO 2008.

Intra-fraction tumor tracking methods can improve radiation delivery during radiotherapy sessions. Image acquisition for tumor tracking and subsequent adjustment of the treatment beam with gating or beam tracking introduces time latency and necessitates predicting the future position of the tumor. This study evaluates the use of multi-dimensional linear adaptive filters and support vector regression to predict the motion of lung tumors tracked at 30 Hz. We expand on the prior work of other groups who have looked at adaptive filters by using a general framework of a multiple-input single-output (MISO) adaptive system that uses multiple correlated signals to predict the motion of a tumor. We compare the performance of these two novel methods to conventional methods like linear regression and single-input, single-output adaptive filters. At 400 ms latency the average root-mean-square-errors (RMSEs) for the 14 treatment sessions studied using no prediction, linear regression, single-output adaptive filter, MISO and support vector regression are 2.58, 1.60, 1.58, 1.71 and 1.26 mm, respectively. At 1 s, the RMSEs are 4.40, 2.61, 3.34, 2.66 and 1.93 mm, respectively. We find that support vector regression most accurately predicts the future tumor position of the methods studied and can provide a RMSE of less than 2 mm at 1 s latency. Also, a multi-dimensional adaptive filter framework provides improved performance over single-dimension adaptive filters. Work is underway to combine these two frameworks to improve performance.

Adaptive 1-D and 2-D Filtering with Internally Passive Structures

Summary Internally passive filters such as wave digital filters (WDF) and orthogonal filters, which have desirable properties, are developed as filter structures for adaptive filters. The equations for updating the multiplier coefficients as well as for computing the gradients are derived for these filters. The stability monitoring during the adaptation process for these filters is simple to implement. Simulation results are included to demonstrate the capability of these filters in system identification and noise cancellation. Moreover, motivated by applications of multidimensional adaptive filters in video compression and image enhancement, the proposed adaptive wave digital filters have been extended to two dimensions and applied as adaptive fan filters. Computer simulations are also conducted to show their potential applications to two-dimensional system identification and image enhancement.

Affine adaptive filtering of CT data

A novel method for resampling and enhancing image data using multidimensional adaptive filters is presented. The underlying issue that this paper addresses is segmentation of image structures that are close in size to the voxel geometry. Adaptive filtering is used to reduce both the effects of partial volume averaging by resampling the data to a lattice with higher sample density and to reduce the image noise level. Resampling is achieved by constructing filter sets that have subpixel offsets relative to the original sampling lattice. The filters are also frequency corrected for ansisotropic voxel dimensions. The shift and the voxel dimensions are described by an affine transform and provides a model for tuning the filter frequency functions. The method has been evaluated on CT data where the voxels are in general non cubic. The in-plane resolution in CT image volumes is often higher by a factor of 3–10 than the through-plane resolution. The method clearly shows an improvement over conventional resampling techniques such as cubic spline interpolation and sinc interpolation.

Adaptive antenna space-time processing techniques to suppress platform scattered clutter for airborne radar

Advanced airborne radar may require adaptive space-time processing (STP) to detect small targets at long ranges. STP is a multidimensional adaptive filter that resolves received radar data into a spectrum of plane waves in angular and Doppler frequency coordinates. The platform of an airborne radar can scatter incident signals into the antenna, spreading the spectra of the clutter signals so that it overlaps the target signal and therefore increases the false alarm rate. To reduce the processing requirements of a full STP filter, a suboptimal architecture with fewer degrees of freedom is demonstrated and compared with the optimal architecture. >

Algorithms and systolic architectures for multidimensional adaptive filtering via McClellan transformations

Algorithms are developed simultaneously with systolic architectures for multidimensional adaptive filtering Because of the extremely high data rate required for real-time video processing, there is a strong motivation to limit the size of any adaptation problem. Combining the McClellan transformations with systolic arrays to adapt and implement the least-squares filter yields a novel solution to the problem of adapting a large zero-phase finite impulse response (FIR) multidimensional filter, having arbitrary directional biases, with only a few parameters. These filters can be adapted abruptly on a block-by-block basis without causing blocking effects. After developing a basic processing element for a systolic array realization of the Chebyshev structure for the McClellan transformation, it is shown that for a given 2-D transformation function, the adaptation of the 1-D prototype filter becomes a small multichannel adaptation problem similar to adaptive array problems. A similar approach is also taken in developing algorithms to adapt the 2-D transformation function. >

Control Measurement in the Presence of Noise† Part I

ABSTRACT In the previous paper a method was derived for making the best use of just one measurement of a parameter or variable, the results being presented in the form of the changes in statistical parameters. In the present paper, the results are generalised to include continuously measured quantities, and the simultaneous estimating of many parameters. The results provide means for designing multi-dimensional adaptive filters, and for determining the state variables of partially observable linear systems.