Discrete Wavelet Transform Algorithm Research Articles

Multiresolution and Multispectral Data Fusion Using Discrete Wavelet Transform with IRS Images: Cartosat-1, IRS LISS III and LISS IV

Image fusion techniques integrate complimentary information from multiple image sensor data such that the new images are more suitable for the purpose of human visual perception and computer based processing tasks for extraction of detail information. As an important part of image fusion algorithms, pixel-level image fusion can combine spectral information of coarse resolution imagery with finer spatial resolution imagery. Ideally, the method used to merge data sets with high-spatial and highspectral resolution should not distort the spectral characteristics of the high-spectral resolution data. This paper describes the Discrete Wavelet Transform (DWT) algorithm for the fusion of two images using different spectral transform methods and nearest neighbor resampling techniques. This research paper investigates the performance of fused image with high spatial resolution Cartosat-1(PAN) with LISS IV and Cartosat-1(PAN) sensor images with the LISS III sensor image of Indian Remote Sensing satellites. The visual and statistical analysis of fused images has shown that the DWT method outperforms in terms of Geometric, Radiometric, and Spectral fidelity.

Successive Image Interpolation Using Lifting Scheme Approach

Problem statement: Fast and accurate interpolation and resizing of images and video frames is a much sought after research area in multimedia applications. The more accurate schemes are computationally expensive and require more time for execution. We proposed here Discrete Wavelet Transform (DWT) using lifting scheme as an accurate and computationally inexpensive interpolation technique for image resizing. Approach: In this study, the lifting scheme DWT algorithm was applied for interpolation of the images to the scale 2-n for reduction in size where n indicated the level of DWT. To magnify the image to the scale 2n, IDWT was used after the zeroeth level DWT, while DWT was used for subsequent reconstruction. Results: In case of reduction in size, the DWT components were calculated to a level so that the four DWT components were reduced to single pixel size and the reconstruction is again carried out to the original size. The reconstruction results were bench marked using Mean Squared Error (MSE) and Peak Signal to Noise Ratio (PSNR) with other schemes like Bilinear and Bicubic interpolations. The two component Harr mother wavelet was found to be suitable for the fast computations of the interpolated images and their subsequent versions. Conclusion: It has been found that after higher level of DWT computations like 10 or 11th level, the MSE increases beyond acceptable limits and the PSNR drops below 20 dB. But the interpolation or reconstruction is completed in much less time with better MSE and PSNR as compared to the bilinear and bicubic scheme. The present technique provided fast interpolation algorithm for multimedia and video processing applications.

Swarm Negative Selection Algorithm for Electroencephalogram Signals Classification

Problem statement: The process of epilepsy diagnosis from EEG signals by a human scorer is a very time consuming and costly task considering the large number of epileptic patients admitted to the hospitals and the large amount of data needs to be scored. Therefore, there is a strong need to automate this process. Such automated systems must rely on robust and effective algorithms for detection and prediction. Approach: The proposed detection system of epileptic seizure in EEG signals is based on Discrete Wavelet Transform (DWT) and Swarm Negative Selection (SNS) algorithm. DWT was used to analyze EEG signals at different frequency bands and statistics over the set of the wavelet coefficients were calculated to introduce the feature vector for SNS classifier. The SNS classification model use negative selection and PSO algorithms to form a set of memory Artificial Lymphocytes (ALCs) that have the ability to distinguish between normal and epileptic EEG patterns. Thus, adapted negative selection is employed to create a set of self-tolerant ALCs. Whereas, PSO is used to evolve these ALCs away from self patterns towards non-self space and to maintain diversity and generality among the ALCs. Results: The experimental results proved that the proposed method reveals very promising performance in classifying EEG signals. A comparison with many previous studies showed that the presented algorithm has better results outperforming those reported by earlier methods. Conclusion: The technique was approved to be robust and effective in detecting and localizing epileptic seizure in EEG recording. Hence, the proposed system can be very helpful to make faster and accurate diagnosis decision.

Merging hyperspectral and panchromatic image data: qualitative and quantitative analysis

Image fusion is one of the most commonly used image enhancement techniques for improving the spatial quality of the source image with minimal spectral distortion in remote sensing. Until now, data fusion algorithms were developed and applied to improve the spatial resolution of the multispectral images and also their performances were evaluated depending on the source images such as Landsat Enhanced Thematic Mapper Plus (ETM+), Landsat Multispectral (MS)/Panchromatic (PAN), Satellite pour l'Observation de la Terre (SPOT) XS/PAN and IKONOS MS/PAN datasets. This paper assesses whether hyperspectral images, having very narrow bands compared to multispectral images, can be fused with high spatial resolution panchromatic images using common and current new algorithms including Intensity‐Hue Saturation (IHS), Principal Component Substitution (PCS), Gram Schmidt Transformation (GST), Smoothing Filter‐based Intensity Modulation (SFIM), Discrete Wavelet Transform (DWT), wavelet‐based IHS (DWT‐IMS) and PCS (DWT‐PCS) and Fast Fourier Transform (FFT)‐enhanced IHS. We also examine the performance of the fused hyperspectral images with respect to the fused multispectral images. For this purpose, two different source datasets (EO1 Hyperion/ALI PAN and EO1 ALI MS/PAN) were used. Some qualitative and quantitative analyses were implemented to assess the spatial and spectral quality of the fused images. The results show that it was possible to carry out the fusion of a narrow‐band hyperspectral image and a high spatial resolution panchromatic image. The fusion of EO1 Hyperion/ALI PAN and EO1 ALI MS/PAN datasets using the SFIM, DWT‐PCS, DWT‐IHS and FFT‐IHS algorithms produces better results than other techniques. Also, the results show that the fusion methods behaved for both datasets in the same performances except the DWT algorithm. The DWT method has a lower performance for the hyperspectral image compared to the multispectral image. Therefore the DWT algorithm should be further studied to improve the spectral qualities of a fused hyperspectral image based on wavelet transformation.

REAL TIME DETECTION OF POWER QUALITY DISTURBANCES IN POWER SYSTEMS

In this study a measurement system has been implemented for detection of power quality disturbances in real time. In the system current and voltage of distribution panel that feeds several loads are measured using a measurement board and then measured values are transferred to the computer via data acquisition board. The obtained data is analysed using the software written in LabVIEW. In developed software FFT(Fast Fourier Transform) algorithm is used for harmonic analysis while DWT(Discrete Wavelet Transform) algorithm is used for determining instantaneous events. Experimental results show that the implemented system is useful not only analysis of current and voltage harmonics but also determining and classification of power quality disturbances such as instantaneous changing, voltage swell, voltage sag and interruptions.

Dynamically reconfigurable systolic array accelerators: a case study with extended Kalman filter and discrete wavelet transform algorithms

Field programmable gate arrays (FPGAs) are increasingly being adopted as the primary on-board computing system for autonomous deep space vehicles. There is a need to support several complex applications for navigation and image processing in a rapidly responsive on-board FPGA-based computer. Developing such a computer requires the designer to explore and combine several design concepts such as systolic array (SA) design, hardware–software partitioning and partial dynamic reconfiguration (PDR). In this study a microprocessor/co-processor design that can simultaneously accelerate multiple single precision floating-point algorithms is proposed. Two such algorithms are extended Kalman filter (EKF) and discrete wavelet transform (DWT). Key contributions include (i) polymorphic systolic array (PolySA), comprising partial reconfigurable regions that can accelerate algorithms amenable to being mapped onto linear SAs and (ii) performance model to predict the overall execution time of EKF algorithm on the proposed PolySA architecture. When implemented on a low-end Xilinx Virtex4 SX35 FPGA, the design provides a speed-up of at least 4.18x and 6.61x over a state-of-the-art microprocessor used in spacecraft systems for the EKF and DWT algorithms, respectively. The performance of EKF algorithm on the proposed PolySA architecture was compared against the performance on two types of conventional (non-polymorphic) hardware architectures and the results showed that the proposed architecture outperformed the other two architectures in most of the test cases.

Discrete Lattice Wavelet Transform

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The discrete wavelet transform (DWT) has gained a wide acceptance in denoising and compression coding of images and signals. In this work we introduce a discrete lattice wavelet transform (DLWT). In the analysis part, the lattice structure contains two parallel transmission channels, which exchange information via two crossed lattice filters. For the synthesis part we show that the similar lattice structure yields a perfect reconstruction (PR) property. The PR condition can be used to design half-band filters, which effectively eliminate aliasing in decimated tree structured wavelet transform. The DLWT can be implemented directly to any of the existing DWT algorithms. </para>

A high-performance and memory-efficient pipeline architecture for the 5/3 and 9/7 discrete wavelet transform of JPEG2000 codec

In this paper, we propose a high-performance and memory-efficient pipeline architecture which performs the one-level two-dimensional (2-D) discrete wavelet transform (DWT) in the 5/3 and 9/7 filters. In general, the internal memory size of 2-D architecture highly depends on the pipeline registers of one-dimensional (1-D) DWT. Based on the lifting-based DWT algorithm, the primitive data path is modified and an efficient pipeline architecture is derived to shorten the data path. Accordingly, under the same arithmetic resources, the 1-D DWT pipeline architecture can operate at a higher processing speed (up to 200 MHz in 0.25-/spl mu/m technology) than other pipelined architectures with direct implementation. The proposed 2-D DWT architecture is composed of two 1-D processors (column and row processors). Based on the modified algorithm, the row processor can partially execute each row-wise transform with only two column-processed data. Thus, the pipeline registers of 1-D architecture do not fully turn into the internal memory of 2-D DWT. For an N/spl times/M image, only 3.5N internal memory is required for the 5/3 filter, and 5.5N is required for the 9/7 filter to perform the one-level 2-D DWT decomposition with the critical path of one multiplier delay (i.e., N and M indicate the height and width of an image). The pipeline data path is regular and practicable. Finally, the proposed architecture implements the 5/3 and 9/7 filters by cascading the three key components.

Adaptive wavelet modelling of a nested 3 factor experimental design in NIR chemometrics

The objective of this study was to investigate the effects of some commonly used sample preparation procedures, including overnight freezing, and the type of homogeniser on the near-infrared (NIR) spectra of red grape homogenates. Homogenates ( n = 284) of three red grape varieties were prepared using one of three types of homogenisers after one of two types of short term storage (fresh and overnight freezing) and then scanned in a FOSS NIRSystems6500 instrument (400–2500 nm). The NIR spectral data were then analysed using various discrimination techniques, namely Penalized Discriminant Analysis (PDA), Multivariate Adaptive Regression Splines discriminant analysis (MARS-DA) and Random Forests (RF) yielding correct classification rates (CCR) of 63.4%, 58.6% and 45.6%, respectively. To improve the CCR of the discrimination models, feature extraction from the NIR spectral data was performed using an adaptive discrete wavelet transformation (DWT). The DWT algorithm employs an adaptive wavelet basis function that maximizes the discrimination between the different combinations of homogenisers, storage and grape varieties. The results after adaptive DWT on the NIR spectra resulted in CCRs of 99.93%, 99.2% and 76.4% for PDA, MARS-DA and RF, respectively. Further analysis of adaptive DWT PDA via MANOVA revealed significant differences in the main and interaction effects of the three treatments, which were then associated with specific regions within the NIR spectrum.

Efficient wavelet prefilters with optimal time-shifts

A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain postfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a enough approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.

A High-Performance and Memory-Efficient Pipeline Architecture for the 5/3 and 9/7 Discrete wavelet Transform of JPEG2000 Codec

In this paper, we propose a high-performance and memory-efficient pipeline architecture which performs the one-level two-dimensional (2-D) discrete wavelet transform (DWT) in the 5/3 and 9/7 filters. In general, the internal memory size of 2-D architecture highly depends on the pipeline registers of one-dimensional (1-D) DWT. Based on the lifting-based DWT algorithm, the primitive data path is modified and an efficient pipeline architecture is derived to shorten the data path. Accordingly, under the same arithmetic resources, the 1-D DWT pipeline architecture can operate at a higher processing speed (up to 200 MHz in 0.25-/spl mu/m technology) than other pipelined architectures with direct implementation. The proposed 2-D DWT architecture is composed of two 1-D processors (column and row processors). Based on the modified algorithm, the row processor can partially execute each row-wise transform with only two column-processed data. Thus, the pipeline registers of 1-D architecture do not fully turn into the internal memory of 2-D DWT. For an N/spl times/M image, only 3.5N internal memory is required for the 5/3 filter, and 5.5N is required for the 9/7 filter to perform the one-level 2-D DWT decomposition with the critical path of one multiplier delay (i.e., N and M indicate the height and width of an image). The pipeline data path is regular and practicable. Finally, the proposed architecture implements the 5/3 and 9/7 filters by cascading the three key components.

Lifting factorization-based discrete wavelet transform architecture design

In this paper, two new system architectures, overlap-state sequential and split-and-merge parallel, are proposed based on a novel boundary postprocessing technique for the computation of the discrete wavelet transform (DWT). The basic idea is to introduce multilevel partial computations for samples near data boundaries based on a finite state machine model of the DWT derived from the lifting scheme. The key observation is that these partially computed (lifted) results can also be stored back to their original locations and the transform can be continued anytime later as long as these partial computed results are preserved. It is shown that such an extension of the in-place calculation feature of the original lifting algorithm greatly helps to reduce the extra buffer and communication overheads, in sequential and parallel system implementations, respectively. Performance analysis and experimental results show that, for the Daubechies (see J.Fourier Anal. Appl., vol.4, no.3, p.247-69, 1998) (9,7) wavelet filters, using the proposed boundary postprocessing technique, the minimal required buffer size in the line-based sequential DWT algorithm is 40% less than the best available approach. In the parallel DWT algorithm we show 30% faster performance than existing approaches.

Measuring the Galaxy Power Spectrum and Scale‐Scale Correlations with Multiresolution‐decomposed Covariance. I. Method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.

Discrete wavelet transform: data dependence analysis and synthesis of distributed memory and control array architectures

We perform a thorough data dependence and localization analysis for the discrete wavelet transform algorithm and then use it to synthesize distributed memory and control architectures for its parallel computation. The discrete wavelet transform (DWT) is characterized by a nonuniform data dependence structure owing to the decimation operation it is neither a uniform recurrence equation (URE) nor an affine recurrence equation (ARE) and consequently cannot be transformed directly using linear space-time mapping methods into efficient array architectures. Our approach is to apply first appropriate nonlinear transformations operating on the algorithm's index space, leading to a new DWT formulation on which application of linear space-time mapping can become effective. The first transformation of the algorithm achieves regularization of interoctave dependencies but alone does not lead to efficient array solutions after the mapping due to limitations associated with transforming the three-dimensional (3-D) algorithm onto one-dimensional (1-D) arrays, which is also known as multiprojection. The second transformation is introduced to remove the need for multiprojection by formulating the regularized DWT algorithm in a two-dimensional (2-D) index space. Using this DWT formulation, we have synthesized two VLSI-amenable linear arrays of LPEs computing a 6-octave DWT decomposition with latencies of M and 2M-1, respectively, where L is the wavelet filter length, and M is the number of samples in the data sequence. The arrays are modular, regular, use simple control, and can be easily extended to larger L and J. The latency of both arrays is independent of the highest octave J, and the efficiency is nearly 100% for any M with one design achieving the lowest possible latency of M.

On the Scalability of 2-D Discrete Wavelet Transform Algorithms

The ability of a parallel algorithm to make efficient use of increasing computational resources is known as its scalability. In this paper, we develop four parallel algorithms for the 2-dimensional Discrete Wavelet Transform algorithm (2-D DWT), and derive their scalability properties on Mesh and Hypercube interconnection networks. We consider two versions of the 2-D DWT algorithm, known as the Standard (S) and Non-standard (NS) forms, mapped onto P processors under two data partitioning schemes, namely checkerboard (CP) and stripped (SP) partitioning. The two checkerboard partitioned algorithms on the cut-through-routed (CT-routed) Mesh are scalable as M^{2}=\Omega(P\log P) (Non-standard form, NS-CP), and as M^{2}=\Omega(P\log^{2}P) (Standard form, S-CP); while on the store-and-forward-routed (SF-routed) Mesh and Hypercube they are scalable as M^2=\Omega(P^{\frac{3}{3-\gamma}}) (NS-CP), and as M^2=\Omega(P^{\frac{2}{2-\gamma}}) (S-CP), respectively, where M^{2} is the number of elements in the input matrix, and \gamma\in (0,1) is a parameter relating M to the number of desired octaves J as J=\lceil \gamma \log M \rceil. On the CT-routed Hypercube, scalability of the NS-form algorithms shows similar behavior as on the CT-routed Mesh. The Standard form algorithm with stripped partitioning (S-SP) is scalable on the CT-routed Hypercube as M^{2}=\Omega(P^{2}), and it is unscalable on the CT-routed Mesh. Although asymptotically the stripped partitioned algorithm S-SP on the CT-routed Hypercube would appear to be inferior to its checkerboard counterpart S-CP, detailed analysis based on the proportionality constants of the isoefficiency function shows that S-SP is actually more efficient than S-CP over a realistic range of machine and problem sizes. A milder form of this result holds on the CT- and SF-routed Mesh, where S-SP would, asymptotically, appear to be altogether unscalable.