Quadratic Volterra Filters Research Articles

Contrast-Enhanced Imaging of Histotripsy Bubble Clouds Using Chirp-Coded Excitation and Volterra Filtering.

Histotripsy is a focused ultrasound therapy that ablates tissue via bubble cloud activity. Real-time ultrasound image guidance is used to ensure safe and effective treatment. Plane-wave imaging enables tracking of histotripsy bubble clouds at a high frame rate but lacks adequate contrast. Furthermore, bubble cloud hyperechogenicity is reduced in abdominal targets, making the development of contrast-specific sequences for deep-seated targets an active area of research. Chirp-coded subharmonic imaging was reported previously to enhance histotripsy bubble cloud detection by a modest 4-6 dB compared to the conventional sequence. Incorporating additional steps into the signal processing pipeline could enhance bubble cloud detection and tracking. In this study, we evaluated the feasibility of combining chirp-coded subharmonic imaging with Volterra filtering for enhancing bubble cloud detection in vitro. Chirped imaging pulses were used to track bubble clouds generated in scattering phantoms at a 1-kHz frame rate. Fundamental and subharmonic matched filters were applied to the received radio frequency signals, followed by a tuned Volterra filter to extract bubble-specific signatures. For subharmonic imaging, the application of the quadratic Volterra filter improved the contrast-to-tissue ratio from 5.18 ± 1.29 to 10.90 ± 3.76 dB, relative to the application of the subharmonic matched filter. These findings demonstrate the utility of the Volterra filter for histotripsy image guidance.

Quadratic Weighted Median Filters for Edge Enhancement of Noisy Images

Quadratic Volterra filters are effective in image sharpening applications. The linear combination of polynomial terms, however, yields poor performance in noisy environments. Weighted median (WM) filters, in contrast, are well known for their outlier suppression and detail preservation properties. The WM sample selection methodology is naturally extended to the quadratic sample case, yielding a filter structure referred to as quadratic weighted median (QWM) that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise. Through statistical analysis of higher order samples, it is shown that, although the parent Gaussian distribution is light tailed, the higher order terms exhibit heavy-tailed distributions. The optimal combination of terms contributing to a quadratic system, i.e., cross and square, is approached from a maximum likelihood perspective which yields the WM processing of these terms. The proposed QWM filter structure is analyzed through determination of the output variance and breakdown probability. The studies show that the QWM exhibits lower variance and breakdown probability indicating the robustness of the proposed structure. The performance of the QWM filter is tested on constant regions, edges and real images, and compared to its weighted-sum dual, the quadratic Volterra filter. The simulation results show that the proposed method simultaneously suppresses the noise and enhances image details. Compared with the quadratic Volterra sharpener, the QWM filter exhibits superior qualitative and quantitative performance in noisy image sharpening.

Generalized orthonormal basis selection for expanding quadratic volterra filters

Volterra models are very useful for signal and system representation due to their general non-linear structure and their property of linearity with respect to the kernels coefficients. However, when using such models we are confronted with a complexity problem that results from the very large number of the kernels coefficients. Expanding the kernels on a generalized orthonormal basis allows to significantly reduce this parametric complexity. In the present paper, a new procedure is proposed for selecting such a generalized orthonormal basis so that a least squares criterion is minimized in the case of a homogeneous quadratic model.

Low-complexity nonlinear adaptive filters for acoustic echo cancellation in GSM handset receivers

High-quality mobile services need to compensate for acoustic echoes that may affect modern cellular phone receivers. To this purpose, adaptive linear filters are generally used since their low complexity allows real-time implementations. However, they often have to identify an acoustic echo path that may contain significant nonlinearities. Therefore, in such cases, a nonlinear model is required. It is well known that Volterra filters are well suited for modeling a large class of nonlinear systems, but they often require too many computational resources for a real-time implementation. The purpose of this paper is twofold. First of all, we propose to use a simplified quadratic Volterra filter, derived taking into account the characteristics of the most important nonlinearities that affect cellular receivers. Second, an efficient adaptation algorithm is derived which extends the Affine Projection (AP) algorithm, proposed for linear filters, to quadratic Volterra filters. This adaptation algorithm offers better convergence and tracking capabilities with respect to the standard LMS and NLMS algorithms. The reduced complexity and the fast adaptation rate make the echo cancellers we are proposing attractive for real-time implementations. Copyright © 2003 AEI.

Detail‐enhanced error diffusion

We propose a modification of the standard error-diffusion technique for image halftoning that enhances edges and textures by reducing the diffusion of the quantization error across edges. It employs a quadratic Volterra filter that extracts features from the original gray- scale image and adapts the feedback loop to the local characteristics of the image. The additional computational complexity is small because the filter only uses a 333 region of support. Experimental comparisons of various techniques show that our modified error diffusion algorithm pro- duces sharper results with improved contrast and detail resolution for both gray-scale and color images. © 1996 Society of Photo-Optical Instrumenta- tion Engineers.

Edge‐enhanced image zooming

A new adaptive algorithm for image interpolation with percep- tual edge enhancement is proposed. Here, perceptual means that edges are enhanced and interpolated in a visually pleasing way. Each pixel neighborhood is classified into one of three categories (constant, ori- ented, or irregular). In each case, an optimal interpolation technique finds the missing pixels without generating unpleasant artifacts such as aliasing or ringing effects. Furthermore, a quadratic Volterra filter is em- ployed to extract perceptually important details from the original image, which are then used to improve the overall sharpness and contrast. Both qualitative and quantitative simulation results clearly show the superiority of our method over standard low-pass interpolation algorithms such as bilinear, diamond-filter, or B-spline interpolation. © 1996 Society of Photo-Optical Instrumentation Engineers. Subject terms: image interpolation; zooming; quadratic Volterra filters; detail en- hancement; image enhancement; edge enhancement.

A general framework for quadratic Volterra filters for edge enhancement

An inherent problem in most image enhancement schemes is the amplification of noise, which, due to Weber's law, is mostly visible in the darker portions of an image. Using a special class of quadratic Volterra filters, we can adapt the enhancement process in a computationally efficient way to the local image brightness because these filters are approximately equivalent to the product of a local mean estimator and a highpass filter. We analyze and derive this subclass of quadratic Volterra filters by investigating the 1-D case first, and then we generalize the results to two dimensions. An important property of these filters is that they map sinusoidal inputs to constant outputs, which allows us to develop a new filter characterization that is more intuitive for our application than the 4-D frequency response. This description finally leads to a novel least-squares design methodology. Image enhancement results using our Volterra filters are superior to those obtained with standard linear filters, which we demonstrate both quantitatively and qualitatively.

Quantification of nonlinear phenomena in laboratory-generated random sea waves

In this paper higher-order statistical signal processing and Volterra series models of nonlinear phenomena are utilized to quantify the role of nonlinear second-order effects in laboratory-generated random seas. It is indicated how higher-order moment spectra may be utilized to determine a frequency-domain Volterra model of the linear and second-order wave physics occurring between two closely spaced points at which the random wave field is sampled. It will be shown that although the amount of ‘‘energy’’ associated with second-order effects is very small, such second-order phenomena play an important role in the generation of large amplitude waves. By inverse Fourier transforming the outputs of the linear and quadratic Volterra filters, it is demonstrated that the generation of large amplitude waves is due to momentary phase locking of the first- and second-order components. All of the phenomena mentioned above will be demonstrated with the aid of experimental data collected at the Offshore Technology Research Center’s Model Basin. [This study was supported by the National Science Foundation Engineering Research Centers Program Grant Number CDR-8721512 through the Offshore Technology Research Center (OTRC). The Volterra modeling techniques were developed under ONR Grant N00014-92-J-1046 and the Joint Services Electronics Program AFOSR F-49620-92-C-0027.]

An efficient approximation to the quadratic Volterra filter and its application in real-time loudspeaker linearization

Nonlinear filtering based on the Volterra series expansion is a powerful and popular approach in signal processing. However, a serious problem is the increased filter complexity as compared to linear filtering. This paper presents an efficient approximation to the second-order Volterra filter. The proposed filter structure, called multi-memory decomposition (MMD), is composed of three linear FIR filters and one multiplier. Hence, the number of required filter operations is linear in the filter memory length. MMD coefficient determination with respect to a second-order reference kernel is presented. Additionally, block-oriented and adaptive algorithms are proposed which calculate the filter weights from input and output measurements of an unknown system. The good performance of the MMD model is demonstrated by simulations and in a real-time application. Therefore, the linearization scheme for the compensation of nonlinear distortions with a preprocessor is introduced. The preprocessor was implemented on a DSP system to reduce the nonlinear distortions of electrodynamic loudspeakers in real-time. The results show the gain in performance if an MMD filter is used instead of a Volterra filter. This is due to the fact that with a given computational power longer memory lengths can be achieved by the MMD model.

Neural network filters for speech enhancement

In adaptive noise cancelling, linear digital filters have been used to minimize the mean squared difference between filter outputs and the desired signal. However, for non-Gaussian probability density functions of the involved signals, nonlinear filters can further reduce the mean squared difference, thereby improving the signal-to-noise ratio at the system output. This is illustrated with a two-microphone beamformer for cancelling directional interference. In the case of a single uniformly distributed interference, we establish the optimum nonlinear performance limit. To approximate optimum performance, we realize two nonlinear filter architectures, the Volterra filter and the multilayer perceptron. The Volterra filter is also examined for speech interference. The beamformer is adapted to minimize the mean squared difference, but performance is measured with the intelligibility weighted gain. This criterion requires the signal-to-noise ratio at the beamformer output. For the nonlinear processor, this can only be determined when no target components exist in the reference channel of the noise canceller so that the target is transmitted without distortion. Under these ideal conditions and at equal filter lengths, the quadratic Volterra filter improves the intelligibility-weighted gain by maximally 2 dB relative to the linear filter.

Bi-impulse response design of isotropic quadratic filters

The bi-impulse response of a 1-D or 2-D quadratic Volterra filter is introduced as a mathematical tool able to completely describe the nonlinear operator. The conditions that must be satisfied in order to obtain isotropic input/output relations are studied. The result is a formal framework that allows simple but effective operators (particularly for image enhancement and preprocessing) to be designed and a deeper insight into the properties of Volterra filters to be acquired. Examples of design and of the performance obtained by processing natural and synthetic images are presented. >

Filter Design for Image Restoration

In this paper an attempt is made to implement the quadratic Volterra filter, which is proposed for Image Restoration and Image Enhancement. Hardware has been designed using iAPX 86 family of components. Software (MSRESTO) has been developed in PL/M86 language so that it can be executed in any system.

Decision-directed nonlinear filter for image processing

A complete quadratic Volterra filter working under the control of a decision algorithm is proposed for image restoration and enhancement. A particular application in the enhancement of images having reduced luminance dynamics is considered.