Multiresolution Wavelet Decomposition Research Articles

Screening of prior refractive surgery by a wavelet-based neural network

Purpose: To demonstrate an objective method of screening for previous refractive surgery using corneal topography. Setting: Corneal topography research laboratories, LSU Eye Center, New Orleans, Louisiana, USA. Methods: Videokeratography (TMS-1, Tomey) examinations from the LSU Eye Center were randomly divided into training and test sets that each included 32 normal corneas and 106 corneas with previous radial keratotomy or photorefractive keratectomy from 1 month up to 10 years after surgery. A set of 1024 axial curvature values were extracted from mires 1 to 25 from each cornea to form a 1-dimensional waveform. Multiresolution wavelet decomposition was performed on this waveform using the s8 Symmlet wavelet. A portion of the resulting wavelet coefficients was input into a backpropagation neural network that was trained to 5% error. After training, the independent test set was passed though the neural net and scored. Results: The trained network correctly recognized 32 of 32 normal corneas and 105 of 106 refractive surgery corneas for a 99.3% accuracy, 99.1% sensitivity, and 100% specificity for previous myopic refractive surgery detection. Conclusions: The 1-dimensional wavelet-based neural network approach was an effective and accurate method of distinguishing eyes that had had myopic refractive surgery from normal eyes. The single error was a result of having too few examples of grossly decentered procedures in the training set.

An adaptive neural-wavelet model for short term load forecasting

This paper proposed a novel model for short term load forecast in the competitive electricity market. The prior electricity demand data are treated as time series. The forecast model is based on wavelet multi-resolution decomposition by autocorrelation shell representation and neural networks (multilayer perceptrons, or MLPs) modeling of wavelet coefficients. To minimize the influence of noisy low level coefficients, we applied the practical Bayesian method Automatic Relevance Determination (ARD) model to choose the size of MLPs, which are then trained to provide forecasts. The individual wavelet domain forecasts are recombined to form the accurate overall forecast. The proposed method is tested using Queensland electricity demand data from the Australian National Electricity Market. (C) 2001 Elsevier Science B.V. All rights reserved.

Food safety inspection using “from presence to classification” object-detection model

With multiresolution decomposition and forest representation of wavelet transforms, we implemented a “from presence to classification” object-detection model. Three aspects of this model are studied. First, the presence of an object is quickly detected with fewer data manipulations at the coarsest resolution; secondly, object classification with high accuracy is fulfilled at the full resolution; and thirdly, the propagation in the coarse-to-fine process is studied in terms of coefficient propagation within a coefficient tree. We applied this model to internal deboned poultry inspection. As soon as the presence of a hazardous object was detected at a coarse resolution, a signal was actuated to reject the chicken fillet containing foreign inclusions before packing. Only with small foreign inclusions did we need to resort to finer resolution analysis.

Multiresolution local contrast enhancement of x-ray images for poultry meat inspection

A multiresolution-analysis-based local contrast transform is proposed to enhance local structures in x-ray images. The local contrast is defined as a ratio of the local intensity variation to the local mean. With wavelet multiresolution decomposition, the detail coefficients and approximation coefficients are interpreted, respectively, as local variations and local averages in virtue of the localization property of wavelet transform. Based on the local contrast transform, an algorithm is developed to modify coefficients before wavelet synthesis. An across-scale local contrast is obtained when the scale associated with the local variation is different from that of the local mean. The nonlinearity and local adaptiveness properties of local contrast transform result in structural enhancement in local dark regions in the reconstructed images. We applied this technique to deboned poultry inspection using x-ray images. Because of its high x-ray absorption, a foreign inclusion appears as a low-intensity object in an x-ray image, thus resulting in contrast enhancement in the reconstructed multiresolution images.

Speed versus quality in low bit-rate still image compression

This paper presents a fast and modied version of the embedded zero-tree wavelet (EZW) coding algorithm that is based on [4,5,15,20] for low bit-rate still image compression applications. The paper presents the trade-o! between the image compression algorithm speed and the reconstructed image quality measured in terms of PSNR. The measurements show a performance speedup by a factor of 6 in average over the EZW [20] and the algorithm presented in [5]. This speedup causes a PSNR degradation of the reconstructed image by 0.8}1.8 dB in average. Nevertheless, the reconstructed image looks &ne’ with no particular visible artifacts even if we have an average degradation of 1 dB in PSNR. The fast algorithm with its achieved speedup is based on consecutive application of three di!erent techniques: (1) Geometric multiresolution wavelet decomposition [15]. It contributes a speedup factor of 4 in comparison to the symmetric wavelet decomposition in [5,20]. It has a prefect reconstruction property which does not degrade the quality. (2) Modied and reduced version of the EZW algorithm for zero-tree coe$cient classication. It contributes a speedup factor of 6 in comparison to the full tree processing in [5,20]. It degrades the quality of the reconstructed image. This includes e$cient multiresolution data representation which enables fast and e$cient traversing of the zero-tree. (3) Exact model coding of the zero-tree coe$cients. It contributes a speedup factor of 15 in comparison to the adaptive modeling in [5]. This is a lossless step which reduces the compression rate because its entropy coder is sub-optimal. The paper presents a detailed description of the above algorithms accompanied by extensive performance analysis. It shows how each component contributes to the overall speedup. The fast compression has an option of manual allocation of compression bits which enables a better reconstruction quality at a pre-selected &zoom’ area. ( 1999 Elsevier Science B.V. All rights reserved.

Complex wavelet-based image mosaics using edge-preserving visual perception modeling

This paper presents a robust panoramic image mosaics scheme in the complex wavelet domain that employs the edge-preserving visual preceptive thresholding techniques. Complex wavelet transform guarantees both the scale and translation invariance for the image alignment, which enables us to calculate the transformation based on the correspondence in the wavelet domain and its application to the original image. The transformation obtained from the wavelet images is sufficiently accurate when applied to the original images due to the scale and translation invariance. In the wavelet domain, the coefficients can be compressed significantly (50–100 : 1 ratios) through the edge-preserving visual perception modeling while the details of the structured information can be retained. The complexity of the transformation calculation on the thresholded wavelet coefficients can be significantly reduced. Moreover, the transformation can be progressively refined through the multiresolution wavelet decomposition. It results in a mosaicking scheme with a great robustness and significantly better performance compared with the traditional mosaicking techniques with no or little loss of the visual quality of the images.

Approximate computation of multidimensional aggregates of sparse data using wavelets

Computing multidimensional aggregates in high dimensions is a performance bottleneck for many OLAP applications. Obtaining the exact answer to an aggregation query can be prohibitively expensive in terms of time and/or storage space in a data warehouse environment. It is advantageous to have fast, approximate answers to OLAP aggregation queries. In this paper, we present a novel method that provides approximate answers to high-dimensional OLAP aggregation queries in massive sparse data sets in a time-efficient and space-efficient manner. We construct a compact data cube , which is an approximate and space-efficient representation of the underlying multidimensional array, based upon a multiresolution wavelet decomposition. In the on-line phase, each aggregation query can generally be answered using the compact data cube in one I/O or a smalll number of I/Os, depending upon the desired accuracy. We present two I/O-efficient algorithms to construct the compact data cube for the important case of sparse high-dimensional arrays , which often arise in practice. The traditional histogram methods are infeasible for the massive high-dimensional data sets in OLAP applications. Previously developed wavelet techniques are efficient only for dense data. Our on-line query processing algorithm is very fast and capable of refining answers as the user demands more accuracy. Experiments on real data show that our method provides significantly more accurate results for typical OLAP aggregation queries than other efficient approximation techniques such as random sampling.

Multiresolution-based image fusion with additive wavelet decomposition

The standard data fusion methods may not be satisfactory to merge high-resolution panchromatic image and low-resolution multispectral image because they can distort the spectral characteristics of the multispectral data. The authors developed technique, based on multiresolution wavelet decomposition, for the merging and data fusion of such images. The method presented consists of adding the wavelet coefficients of the high-resolution image to the multispectral (low-resolution) data. They have studied several possibilities concluding that the method which produces the best results consists in adding the high order coefficients of the wavelet transform of the panchromatic image to the intensity component (defined as L=(R+G+B)/3) of the multispectral image. The method is, thus, an improvement on standard intensity-hue-saturation (IHS or LHS) mergers. They used the a trous algorithm which allows the use of dyadic wavelet to merge nondyadic data in simple and efficient scheme. They used the method to merge SPOT and LANDSAT/sup TM/ images. The technique presented is clearly better than the IHS and LHS mergers in preserving both spectral and spatial information.

Image fusion with additive multiresolution wavelet decomposition Applications to SPOT+Landsat images

A technique based on multiresolution wavelet decomposition was developed for the merging and data fusion of a high-resolution panchromatic image and a low-resolution multispectral image. The standard data fusion methods may not be satisfactory, because they can distort the spectral characteristics of the multispectral data. The method presented here consists of adding the wavelet coefficients of the high-resolution image to the multispectral (low-resolution) data. More specifically, we add the high-order coefficients of the wavelet transform of the panchromatic image to the intensity component (L) of the multispectral image. The method is thus an improvement on standard intensity–hue–saturation (IHS or LHS) mergers. An alternative approach for correcting the red–green–blue coefficients is also discussed. We used the method to merge SPOT and Landsat Thematic Mapper images (SPOT means Système pour l’Observation de la Terre). The technique presented is clearly better than the IHS and LHS mergers for preserving both spectral and spatial information.

Wavelet-based histograms for selectivity estimation

Query optimization is an integral part of relational database management systems. One important task in query optimization is selectivity estimation, that is, given a query P , we need to estimate the fraction of records in the database that satisfy P . Many commercial database systems maintain histograms to approximate the frequency distribution of values in the attributes of relations. In this paper, we present a technique based upon a multiresolution wavelet decomposition for building histograms on the underlying data distributions, with applications to databases, statistics, and simulation. Histograms built on the cumulative data distributions give very good approximations with limited space usage. We give fast algorithms for constructing histograms and using them in an on-line fashion for selectivity estimation. Our histograms also provide quick approximate answers to OLAP queries when the exact answers are not required. Our method captures the joint distribution of multiple attributes effectively, even when the attributes are correlated. Experiments confirm that our histograms offer substantial improvements in accuracy over random sampling and other previous approaches.

Interframe coding using two-stage variable block-size multiresolution motion estimation and wavelet decomposition

We propose a two-stage variable block-size multiresolution motion estimation (MRME) algorithm. In this algorithm, a method to reduce the amount of motion information is developed, and a bit allocation method minimizing the sum of the motion information and the prediction error is obtained in the wavelet transform domain. In the first stage of the proposed scheme, we utilize a set of wavelet components of the four subbands in the lowest resolution. These motion vectors are directly used as motion vectors for the lowest subband, and are scaled into the initial biases for other subbands at every layer of the wavelet pyramid. In the second stage, the bottom-up construction of a quadtree based on the merge operation is performed. The proposed scheme reduces the uncompressed bit rate of 8 bits/pixel into 0.212 bits/pixel at 41.1 dB of PSNR for the "Claire" sequence, which can be regarded as nearly an 11% reduction compared with the conventional method.

Multiresolution wavelet decomposition of the seismocardiogram

The seismocardiogram (SCG) is a complex, nonstationary signal used for pathological analysis of cardiac vibratory activity. This article reports the results of multiresolution wavelet decomposition of SCGs for a normal male subject, pertaining to three different physiological conditions. Marked differences in certain sub-bands are discernible, which are undetectable in the time-domain alone.

Periodic wavelets

Definitions of multiresolution analysis and wavelet decomposition for a wide range of quasi-Banach spaces of periodic distributions are suggested. Elementary properties of such MRAs are investigated. Economical algorithms of wavelet decomposition and reconstruction are presented.

Simultaneous image fusion and reconstruction using wavelets applications to SPOT + LANDSAT images

In this paper we present a technique, based on multiresolution wavelet decomposition, for the merging and data fusion of two images. The images to merge are a high-resolution panchromatic image and a low-resolution multispectral image. The method consists of adding the wavelet coefficients of the high-resolution image to the multispectral (low-resolution) data. We applied the method to merge SPOT and LANDSAT (TM) images. The current data fusion methods may not be satisfying because they can distort the spectral characteristics of the multispectral data. The technique presented here is clearly better than the standard IHS and LHS mergers in preserving both spectral and spatial information. The fusion of reconstructed images and the application of the technique to astronomical images are commented on.

A restoration algorithm for P-32 and Y-90 bremsstrahlung emission nuclear imaging: a wavelet-neural network approach.

A novel wavelet-based neural network (WNN) filter is proposed for image restoration as required for imaging of beta emitters by bremsstrahlung detection using a gamma camera. Quantitative imaging of beta emitters is important for the in vivo management of antibody therapy using either P-32 or Y-90. The theoretical basis for the general case for M-channel multiresolution wavelet decomposition of the nuclear image into different subimages is developed with the objective of isolating the signal from noise. A modified Hopfield neural network (NN) architecture is then used for multichannel image restoration using the dominant signal subimages. The NN model avoids the common inverse problem associated with other image restoration filters such as the Wiener filter. The relative performance of the WNN for image restoration, for M = 2 channel, is compared to a previously reported order statistic neural network hybrid (OSNNH) filter. Initially simulated degraded images of known structures with different noise levels are used. Quantitative metrics such as the normalized mean square error (NMSE) and signal-to-noise ratio (SNR) are used to compare filter performance. The WNN yields comparable results for image restoration with suggested slightly better performance for the images with higher noise levels as often encountered in bremsstrahlung detection. Attenuation measurements were performed using two radionuclides, 32P and 90Y as required for calibration of the gamma camera for quantitative measurements. Similar values for an effective attenuation coefficient were observed for the restored images using the OSNNH filters (32P: mu = 0.122 cm-1, 90Y: mu = 0.135 cm-1) and WNN (32P: mu = 0.122 cm-1, 90Y: mu = 0.135 cm-1) filters with slightly higher values obtained for the raw data (32P: mu = 0.142 cm-1, 90Y: mu = 0.142 cm-1) for a 3.5-cm source size. The WNN, however, was computationally more efficient by a factor of 4 to 6 compared to the OSNNH filter. The filter architecture, in turn, is also optimum for parallel processing or VLSI implementation as required for planar and particularly for SPECT mode of detection.

Artifacts in wavelet image merging

Intensity modulation (IM), intensity-hue-saturation (IHS), and multiresolution wavelet decomposition (MWD) are {ital ad} {ital hoc} image merging techniques that enhance low-spatial-resolution color imagery with high-resolution black and white imagery. While the MWD is a relatively new technique, both IM and IHS can be found in commercial software. These three merging techniques are compared to find which best retains spectral fidelity while adding spatial information. With this criterion, merging artifacts are identified and characterized. Specifically, the three techniques were tested with respect to resampling, misregistration, intensity variance, and complexity problems that arise in multiresolution image merging. Test images were used allowing the mean difference, standard deviation difference, entropy difference, and affected area to be calculated. {copyright} {ital 1996 Society of Photo{minus}Optical Instrumentation Engineers.}

Wavelet-based neural network with fuzzy-logic adaptivity for nuclear image restoration

A novel wavelet-based neural network with fuzzy-logic adaptivity (WNNFA) is proposed for image restoration using a nuclear medicine gamma camera based on the measured system point spread function. The objective is to restore image degradation due to photon scattering and collimator photon penetration with the gamma camera and allow improved quantitative external measurements of radionuclides in vivo. The specific clinical model proposed is the imaging of bremsstrahlung radiation using /sup 32/P and /sup 90/Y. The theoretical basis for four-channel multiresolution wavelet decomposition of the nuclear image into different subimages is developed with the objective of isolating the signal from noise. A fuzzy rule is generated to train a membership function using least mean squares to obtain an optimal balance between image restoration and the stability of the neural network, while maintaining a linear response for the camera to radioactivity dose. A multichannel modified Hopfield neural network architecture is then proposed for multichannel image restoration using the dominant signal subimages.

Image merging and data fusion by means of the discrete two-dimensional wavelet transform

A new technique is developed for the merging and data fusion of two images. Two spatially registered images with differing spatial resolutions and color content are merged by combining multiresolution wavelet-decomposition components from each and then reconstructing the merged image by means of the inverse wavelet transform. The wavelet merger can employ a variety of wavelet bases, but in presentation of the concept, simple orthonormal sets—Haar and Daubechies wavelets—are explored. The wavelet technique is compared with the intensity–hue–saturation merging technique by means of multispectral and panchromatic test images. The results of the comparison show the wavelet merger performing better in combining and preserving spectral–spatial information for the test images.

Multiscale Wiener filter for the restoration of fractal signals: wavelet filter bank approach

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter is proposed in this paper for signal restoration of 1/f family of fractal signals which are distorted by the transmission channel and corrupted by external noise. First, the fractal signal transmission process is transformed via the analysis filter bank into multiscale convolution subsystems in time-scale domain based on orthonormal wavelets. Some nonstationary properties, e.g., self-similarity, long-term dependency of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals. Then the estimated multiscale input signals are synthesized to obtain the estimated input signal. Some simulation examples are given for testing the performance of the proposed algorithm. With this multiscale analysis/synthesis design via the technique of the wavelet filter bank, the multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals. >

Multiscale video representation using multiresolution motion compensation and wavelet decomposition

A multiscale video representation using wavelet decomposition and variable-block-size multiresolution motion estimation (MRME) is presented. The multiresolution/multifrequency nature of the discrete wavelet transform makes it an ideal tool for representing video sources with different resolutions and scan formats. The proposed variable-block-size MRME scheme utilizes motion correlation among different scaled subbands and adapts to their importance at different layers. The algorithm is well suited for interframe HDTV coding applications and facilitates conversions and interactions between different video coding standards. Four scenarios for the proposed motion-compensated coding schemes are compared. A pel-recursive motion estimation scheme is implemented in a multiresolution form. The proposed approach appears suitable for the broadcast environment where various standards may coexist simultaneously. >