Homomorphic Filtering Research Articles

Cepstral coefficients, covariance lags, and pole-zero models for finite data strings

One of the most widely used methods of spectral estimation in signal and speech processing is linear predictive coding (LPC), LPC has some attractive features, which account for its popularity, including the properties that the resulting modeling filter (i) matches a finite window of n+1 covariance lags, (ii) is rational of degree at most n, and (iii) has stable zeros and poles. The only limiting factor of this methodology is that the modeling filter is "all-pole," i.e., an autoregressive (AR) model. In this paper, we present a systematic description of all autoregressive moving-average (ARMA) models of processes that have properties (i)-(iii) in the context of cepstral analysis and homomorphic filtering. We show that each such an ARMA model determines and is completely determined by its finite windows of cepstral coefficients and covariance lags. We show that these nth-order windows form local coordinates for all ARMA models of degree n and that the pole-zero model can be determined from the windows as the unique minimum of a convex objective function. We refine this optimization method by first noting that the maximum entropy design of an LPC filter is obtained by maximizing the zeroth cepstral coefficient, subject to the constraint (i). More generally, we modify this scheme to a more well-posed optimization problem where the covariance data enter as a constraint and the linear weights of the cepstral coefficients are "positive"-in a sense that a certain pseudo-polynomial is positive-rather succinctly generalizing the maximum entropy method. This new problem is a homomorphic filter generalization of the maximum entropy method. providing a procedure for the design of any stable, minimum-phase modeling filter of degree less or equal to n that interpolates the given covariance window. We present an algorithm for realizing these filters in a lattice-ladder form, given the covariance window and the moving average part of the model, While we also show how to determine the moving average part using cepstral smoothing, one can make use of any good a priori estimate for the system zeros to initialize the algorithm. We conclude the paper with an example of this method, incorporating an example from the literature on ARMA modeling.

Homomorphic cameo filter for pattern recognition that is invariant with changes in illumination

We introduce a new matched filter method that yields correlation peaks that are invariant with changes in the illumination of any targets. A scene containing objects at unknown locations is first subjected to a logarithmic transformation that changes the multiplicative constant to an additive background, which is then discriminated against by means of a composite filter containing a cameo of the true target and a term with which to discriminate against other false targets. Experimental results are shown.

Image Enhancement using Logarithmic Image Processing Model

Image enhancement process consist of a collection of techniques that seek to improve the visual appearance of an image, or to convert the image to a form better suited for analysis by a human visual system or for machine perception. In many practical situations, the illumination of a scene is changing with space and time. It is not unusual to have images having brightly lit and shadowed portions in the same scene demanding information extraction from the entire image. For example in the instance of space images over mountainous terrain you find brightly lit portions facing the sun while the other portion remain in the dark. Techniques based on homomorphic filtering are useful in these cases. However, these are based on spatial frequency filtering and tend to perform poorly in low SNR portion of the image.Up to now, image processing and image analysis have borrowed their basic tools from functional analysis like Fourier filtering, differential and integral calculus etc, these tools are very efficient when they are put in a well defined algebraic frame, unfortunately all images does not have the same structure. The logarithmic image processing (LIP) model is a mathematical framework which provides a specific set of algebraic and functional operations for the processing and analysis of intensity images valued in a bounded range. The LIP model is consistent with the multiplicative transmittance and reflectance image formulation model, and with some important laws and characteristic of human brightness perception. This article addresses the Lee's image enhancement algorithm in a different approach. This approach, based on LIP model can simultaneously enhance the overall contrast and the sharpness of an image. The algorithm is shown to be capable of enhancing the details in the dark as well as bright areas of digital image and at the same time obtains improved overall contrast.

CEPSTRAL PREDICTION ANALYSIS OF THE SIGNAL PATHWAY IN AN ULTRASONIC A-SCAN

Digital deconvolution of ultrasonic echo signals improves resolution and the quality of ultrasonic images. The Homomorphic deconvolution technique under noisy conditions is applied to simulation results in an ultrasonic pulse–echo amplitude scan line. The simulation includes radiation coupling and transducer response, as well as frequency-dependent absorption in the field medium. An accurate method of estimating the pulse-shaping effects of the transducer and the test medium are developed by using Homomorphic filtering. Experimental results are given which confirm the modelling.

Comparametric equations with practical applications in quantigraphic image processing

It is argued that, hidden within the flow of signals from typical cameras, through image processing, to display media, is a homomorphic filter. While homomorphic filtering is often desirable, there are some occasions where it is not. Thus, cancellation of this implicit homomorphic filter is proposed, through the introduction of an antihomomorphic filter. This concept gives rise to the principle of quantigraphic image processing, wherein it is argued that most cameras can be modeled as an array of idealized light meters each linearly responsive to a semi-monotonic function of the quantity of light received, integrated over a fixed spectral response profile. This quantity depends only on the spectral response of the sensor elements in the camera. A particular class of functional equations, called comparametric equations, is introduced as a basis for quantigraphic image processing. These are fundamental to the analysis and processing of multiple images differing only in exposure. The "gamma correction" of an image is presented as a simple example of a comparametric equation, for which it is shown that the underlying quantigraphic function does not pass through the origin. Thus, it is argued that exposure adjustment by gamma correction is inherently flawed, and alternatives are provided. These alternatives, when applied to a plurality of images that differ only in exposure, give rise to a new kind of processing in the "amplitude domain". The theoretical framework presented in this paper is applicable to the processing of images from nearly all types of modern cameras. This paper is a much revised draft of a 1992 peer-reviewed but unpublished report by the author, entitled "Lightspace and the Wyckoff principle."

10.1162/jmlr.2003.4.7-8.1499

It is well known that even slight changes in nonuniform illumination lead to a large image variability and are crucial for many visual tasks. This paper presents a new ICA related probabilistic model where the number of sources exceeds the number of sensors to perform an image segmentation and illumination removal, simultaneously. We model illumination and reflectance in log space by a generalized autoregressive process and Hidden Gaussian Markov random field, respectively.The model ability to deal with segmentation of illuminated images is compared with a Canny edge detector and homomorphic filtering. We apply the model to two problems: synthetic image segmentation and sea surface pollution detection from intensity images.

Nonlinear filtering of backpropagated fields

As a result of interest in imaging strongly scattering targets, the Air Force Research Laboratory is making available to the community sets of data from various targets. We describe a nonlinear filtering technique, namely, homomorphic filtering, which we have applied to recover an image of the target from the backpropagated field calculated from the scattering data. We show new results for targets that other methods, especially linearized methods, are unable to image. While we obtain good images with real data, convolutional effects arising from limited data can sometimes degrade performance.

Diffraction Tomography of Strongly Scattering Objects Based on Homomorphic Filtering

3-D plots of the output space are shown in the lower part of Figure 1. Each 3-D plot presents the transverse intensity distribution at some z0 along the longitudinal axis. The two strong correlation peaks on planes z0 = -2 and 1 indicate the locations of the two recognized vehi­ cles, which are identical to the reference. In conclusion, our (3-D) optical correlator opens op­ portunities to process 3-D images directly and rapidly. Therefore, targets distributed in 3-D space can be recog­ nized or tracked by optical correlators in the same fast

Review and evaluation of MRI nonuniformity corrections for brain tumor response measurements.

Current MRI nonuniformity correction techniques are reviewed and investigated. Many approaches are used to remedy this artifact, but it is not clear which method is the most appropriate in a given situation, as the applications have been with different MRI coils and different clinical applications. In this work four widely used nonuniformity correction techniques are investigated in order to assess the effect on tumor response measurements (change in tumor volume over time): a phantom correction method, an image smoothing technique, homomorphic filtering, and surface fitting approach. Six brain tumor cases with baseline and follow-up MRIs after treatment with varying degrees of difficulty of segmentation were analyzed without and with each of the nonuniformity corrections. Different methods give significantly different correction images, indicating that rf nonuniformity correction is not yet well understood. No improvement in tumor segmentation or in tumor growth/shrinkage assessment was achieved using any of the evaluated corrections.

WAVE PROPAGATION THROUGH SOILS IN CENTRIFUGE TESTING

Wave propagation phenomena in soils can be experimentally simulated using centrifuge scale models. An original excitation device (drop-ball arrangement) is proposed to generate short wave trains. Wave reflections on model boundaries are taken into account and removed by homomorphic filtering. Propagation is investigated through dispersion laws. For drop-ball experiments, spherical wave field analysis assuming linear viscoelasticity leads to a complete analytical description of wave propagation. Damping phenomena are examined and evaluated using this description.

Wave propagation through soils in centrifuge testing

Wave propagation phenomena in soils can be experimentally simulated using centrifuge scale models. An original excitation device (drop-ball arrangement) is proposed to generate short wave trains. Wave reflections on model boundaries are taken into account and removed by homomorphic filtering. Propagation is investigated through dispersion laws. For drop-ball experiments, spherical wave field analysis assuming linear viscoelasticity leads to a complete analytical description of wave propagation. Damping phenomena are examined and evaluated using this description.

Complex cepstral filtering of images and echo removal in the radon domain

Homomorphic filtering using the complex cepstrum has been used in many applications of one-dimensional (1D) signal processing, notably speech and seismic signal analysis. Some work has been done in extending cepstral filtering to the 2D domain. An application that we are particularly interested in is 2D echo removal. We show in this paper that 1D cepstral filtering techniques may be applied to the projections of images in the Radon domain. The filtered projections may then be used to reconstruct an image without the echoes. Results with synthetic images are presented to illustrate the strengths of the method. The technique could find applications in analysis of textured images and images obtained via reconstruction from projections.

Optimum filter for detecting a target in multiplicative noise and additive noise

We derive an optimum filter function to detect a target degraded by multiplicative noise and additive overlapping noise and placed in background noise. The filter is designed to maximize the metric peak-to-output energy, which is the ratio of the expected value squared of the output peak at the target position to the expected value of the average output energy. The optimum filter provides improved discrimination as well as robustness to input noise. One advantage of the filter described here over the homomorphic filters is that the additional preprocess on the input image, that is, the input logarithmic operation, is not required for reducing the effects of multiplicative noise. The performance of the filter is examined in terms of discrimination against background noise and robustness to multiplicative and additive input noise. Both multiplicative amplitude noise and multiplicative complex noise are considered.

Practical considerations on color image enhancement using homomorphic filtering

We present a study concerning the practical possibilities of using the homomorphic filtering for color image enhancement. Two of the most popular color models, RGB and C-Y (color difference), are employed and the results are comparatively discussed. The homomorphic filtering has proven to be a viable tool for both color models considered.

Iterative homomorphic technique for speckle reduction in synthetic-aperture radar imaging

The presence of speckle in radar images reduces the radiometric resolution and renders less efficient the procedures for texture class discrimination. We present an algorithm devoted to speckle reduction in syntheticaperture radar images based on a homomorphic filter coupled with a Wiener filter. To construct the Wiener filter we analytically evaluate the autocorrelation function of the noise, starting from the first two orders of statistics of the noise, before performing the homomorphic transformation (a logarithmic one, in the case of multiplicative noise), and the autocorrelation of the noise-free image is evaluated by an iterative procedure. The algorithm, tested on both simulated and actual synthetic-aperture radar images, provides very promising results and shows the usefulness of the proposed method.

Neutron penumbral imaging of inertial confinement fusion targets at Phébusa)

First 14 MeV neutron images of imploded microballoons have been obtained at the Phébus laser facility at CEL-V in 1992 [Garconnet et al. Laser Part Beams 11, 3 (1994)]. The sizes of the neutron source have been measured by using a coded-aperture imaging system and a scintillator array as a detector. The threshold of the experimental setup was typically 2×1010 neutrons/shot. 600–800 μm source sizes in direct drive experiments have been measured with a 130 μm two-point resolution. In 1993 we improved the sensitivity of the camera by increasing the light collection efficiency. It can now work at a neutron yield as small as a few 108. Thanks to this improvement some images in indirect drive experiments have been recorded in the range 3×108–5×109 with a 56 μm two-point resolution. Wiener filter, homomorphic Wiener filter, and Nugent’s ‘‘comb filter’’ methods have been used and compared to deconvolve the penumbral images. Design of the camera and numerical method performances will be discussed.

Neutron penumbral imaging of inertial confinement fusion targets at Phébus (abstract)a)

First 14 MeV neutron images of imploded microballoons have been obtained on the Phebus laser facility at CEL-V in 1992 [Garconnet et al. Laser Part Beams 11, 3 (1994)]. The sizes of the neutron source have been measured by using a coded-aperture imaging system and a scintillator array as a detector. The threshold of the experimental setup was typically 2×1010 neutrons/shot. 600–800 μm source sizes in direct drive experiments have been measured with a 130 μm two-point resolution. In 1993 we improved the sensitivity of the camera by increasing the light collection efficiency. It can now work at a neutron yield as small as a few 108. Thanks to this improvement some images in indirect drive experiments have been recorded in the range 3⋅108–5⋅109 with a 56 μm two-point resolution. Wiener filter, homomorphic Wiener filter, and Nugent’s ‘‘comb filter’’ methods have been used and compared to deconvolve the penumbral images. Design of the camera and numerical method performances will be discussed.

A homomorphic filtering method for imaging strongly scattering penetrable objects

This paper describes a new method for determining the structure of strongly scattering penetrable objects having permittivity fluctuations with scales comparable to the illuminating wavelength. We are concerned with the case when small wavelength or weakly scattering approximations, such as the Born or distorted wave Born approximations, or slowly varying approximations such as the Rytov approximation, are not valid. The problem is formulated as one of recovering, in principle, a quantitative image of the object's permittivity distribution function from a set of perturbed images. Each perturbed image is obtained by backpropagating the scattered field measured around the object for different illumination directions. These backpropagated images are filtered in the differential cepstral domain to recover the object permittivity distribution, and we show reconstructions from both simulated and real microwave scattered data. >

Hardware realization of a 2D IIR semisystolic filter with application to real-time homomorphic filtering

Hardware design and implementation of a 2D sample-and-hold semisystolic filter structure are presented. Log and antilog circuits are used with a high-frequency-emphasis IIR filter to provide homomorphic filtering. SPICE simulation using functional blocks as well as particulars on the hardware design with reference to specific device types and characteristics are discussed. A hardware prototype circuit using MSI and LSI circuits on a custom-made PCB is shown along with applications to real-time filtering of broadcasted TV images. >

Real-time 2-D homomorphic filter for broadcast TV signals

Hardware design and implementation of a 2-D sample- and-hold semisystolic filter structure are presented. Log and antilog circuits are utilized with a high-frequency emphasis IIR (infinite impulse response) filter to provide homomorphic filtering. Hardware design is discussed with reference to specific device types and characteristics. A prototype circuit using MSI and MSI circuits on a custom-made PCB (printed circuit board) is shown along with applications to real-time filtering of broadcast TV images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>