In this paper, we present a new state space-based approach for the two-dimensional (2-D) frequency estimation problem which occurs in various areas of signal processing and communication problems. The proposed method begins with the construction of a state space model associated with the noiseless data which contains a summation of 2-D harmonics. Two auxiliary Hankel-block-Hankel-like matrices are then introduced and from which the two frequency components can be derived via matrix factorizations along with frequency shifting properties. Although the algorithm can render high resolution frequency estimates, it also calls for lots of computations. To alleviate the high computational overhead required, a highly parallelizable implementation of it via the principle subband component (PSC) of some appropriately chosen transforms have been addressed as well. Such a PSC-based transform domain implementation not only reduces the size of data needed to be processed, but it also suppresses the contaminated noise outside the subband of interest. To reduce the computational complexity induced in the transformation process, we also suggest that either the transform of the discrete Fourier transform (DFT) or the Haar wavelet transform (HWT) be employed. As a consequence, such an approach of implementation can achieve substantial computational savings; meanwhile, as demonstrated by the provided simulation results, it still retains roughly the same performance as that of the original algorithm.

The defects in the cold rolled strips have textural characteristics, which are nonuniform due to its irregularities and deformities in geometrical appearance. In order to handle the textural characteristics of images with defects, this paper proposes a surface inspection method based on textural feature extraction using the wavelet transform. The wavelet transform is employed to extract local features from textural images with defects both in the frequency and in the spatial domain. To extract features effectively, an adaptive wavelet packet scheme is developed, in which the optimum number of features are produced automatically through subband coding gain. The energies for all subbands of the optimal quadtree of the adaptive wavelet packet algorithm and four entropy features in the level one LL subband, which correspond to the local features in the spatial domain, are extracted. A neural network is used to classify the defects of these features. Experiments with real image data show good training and generalization performances of the proposed method.

In audio-frequency magnetotelluric surveys, electromagnetic radiation from worldwide thunderstorm activity is used as an energy source for geophysical exploration. Owing to its origin, such a signal is inherently transient and short lived. Therefore, special care should be taken in the detection and processing of this transient signal because the interval of time between two successive transient events contains almost no information as far as the audio frequency magnetotellurist is concerned. In this paper, a wavelet transform detection, processing and analysis technique is developed. A complex-compactly-supported wavelet, known as the Morlet wavelet, is selected as the mother wavelet. With the Morlet wavelet, lightning transients can be easily identified in the noisy recordings and the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. This scheme has been tested on real data collected in the archipelago of Svalbard, Norway as well as on five sets of synthetic data contaminated with various kinds of noise. The results show the superior performance of the wavelet transform transient detection and analysis technique.

A new method to obtain the coefficients of Daubechies's scaling functions is given, in which it is not necessary to find the complex zeros of polynomials. Consequently it becomes easier to obtain the coefficients of arbitrary order from 2 to 40 with high accuracy.

A method of planar curve classification, which is invariant to rotation, scaling and translation using the zerocrossings representation of wavelet transform was introduced. The description of the object is represented by taking a ratio between its two adjacent boundary points so it is invariant to object rotation, translation and size. Transforming this signal to zero-crossings representation using wavelet transform, the minimum distance between the object and model while shifting the signals each other, can be used as classification parameter.

In this paper, new wavelet bases are presented. We address problems associated with the proposed matched filter in multirate systems, using an optimum receiver that maximises the SNR at the sampling instant. To satisfy the Nyquist (ISI-free transmission) and matched filter (maximum SNR at the sampling instant) criteria, the overall system filtering strategy requires to split the narrowest filter equally between transmitter and receiver. In data transmission systems a raised-cosine filter is therefore often used to bandlimit signals from which wavelet bases are derived. Sampling in multiresolution subspaces is also discussed.

This paper is concened with the design and implementation of a 2-channel, 2-dimensional filter bank using rectangular (analog/digital) and quincunx (digital/digital) sampling. The associated analog low-pass filters are separable where as the digital low-pass filters are non-separable for a minimum sampling density requirement. The digital low-pass filters are Butterworth type filters, N = 9, realized as LWDFs. They, when itterated, approximate a valid scaling function (raised-consine scaling function). The obtained system can be used to compute a discrete wavelet transform.

The millimeter wave (MMW) radar has good compromise characteristics of both microwave radar and optical sensors. It has better angular and range resolving abilities than microwave radar, and a longer penetrating range than optical sensors. We used the MMW radar to detect targets located in the sea and among sea ice clutter based on fractals, wavelets, and neural networks. The wavelets were used as feature extractors to decompose the MMW radar images and to extract the feature vectors from approximation signals at different resolution levels. Unsupervised neural classifiers with parallel computational architecture were used to classify sea ice, sea water and targets based on the competitive learning algorithm. The fractal dimensions could provide a quantitative description of the roughness of the radar image. Using these techniques, we can detect targets quickly and clearly discriminate between sea ice, sea water, and targets.

For very low bit-rate video coding such as under 64 kbps, it is unreasonable to encode and transmit all the information. Thus, it is very important to choose the "important" information and encode it efficiently. In this paper, we first propose an image separation-composition method to solve this problem. At the encoder, an image is separated into a low-frequency part and two (horizontal and vertical) edge parts, which are considered as "important" information for human visualization. The low-frequency part is encoded by using block DCT and linear quantization. And the edges are selected by their values and encoded by using Chain coding to remain the most of the important parts for human visualization. At the decoder, the image is reconstructed by first generating the high-frequency parts from the horizontal and vertical edge parts, respectively, and then applying the inverse wavelet transform to the low frequency part and high frequency parts. This composition algorithm has less computational complexity than the conventional analytic/synthetic algorithms because it is not based on iterating approach. Moreover, to reduce the temporal redundancy efficiently, we propose a hierarchical motion detection and a motion interpolation /extrapolation algorithm. We detect motion vectors and motion regions between two reconstructed images and then predict the motion vectors of the current image from the previous detected motion vectors and motion regions by using the interpolation/extrapolation both at the encoder and at the decoder. Therefore, it is unnecessary to transmit the motion vectors and motion regions. This algorithm reduces not only the temporal redundancy but also bit-rates for coding side information . Furthermore, because the motion detection is completely syntax independent, any type of motion detection can be used. We show some simulation results of the proposed video coding algorithm with the coding bit-rate down to 24 kbps and 10 kbps.

Research in very low-bit rate coding has made significant advancements in the past few years. Most recently, the introduction of the MPEG-4 proposal has motivated a wide variety of a approaches aimed at achieving a new level of video compression. In this paper we review progress in VLBV categorized into 3 main areas. (1) Waveform coding, (2) 2D Content-based coding, and (3) Model-based coding. Where appropriate we also described proposals to the MPEG-4 committee in each of these areas.

We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.

Two drawbacks of pyramidal wavelet transforms for finite-length sequences are the lack of conservation of the support and the boundary effect. In this letter, the structure of cyclic wavelet transforms (CWT) is used to permute the input and output data to map them into a linear array. Systolic realization of cyclic wavelet packet transforms (CWPT) is also presented to adequately deal with finite-length sequences which have dominant information on high or median frequency channels. The VLSI architectures designed in this letter are very attractive because adaptive processing can be achieved by just programming the filter coefficients.

A new adaptive AR spectral estimation method is proposed. While conventional least-squares methods use a single windowing function to analyze the linear prediction error, the proposed method uses a different window for each frequency band of the linear prediction error to define a cost function to be meinemized. With this approach, since time and frequency resolutions can be traded off throughout the frequency spectrum, an improvement on the precision of the estimates is achieved. In this paper, a wavelet-like time-frequency resolution grid is used so that low-frequency components of the linear prediction error are analyzed through long windows and high-frequency components are analyzed through short ones. To solve the optimization problem for the new cost function, special properties of the correlation matrix are used to derive an RLS algorithm on the order of M2, where M is the number of parameters of the AR model. Computer simulations comparing the performance of conventional RLS and the proposed methods are shown. In particular, it can be observed that the wavelet-based spectral estimation method gives fine frequency resolution at low frequencies and sharp time resolution at high frequencies, while with conventional methods it is possible to obtain only one of these characteristics.

The purpose of this paper is to provide a practical tool for performing a shift operation in orthonormal compactly supported wavelet bases. This translation τ of a discrete sequence, where τ is a real number, is suitable for filter bank implementations. The shift operation in this realization is neither related to the analysis filters nor to the synthesis filters of the filter bank. Simulations were done on the Daubechis wavelets with 12 coefficients and on complex valued wavelets. For the latter ones a real input sequence was used and split up into two subsequences in order to gain computational efficiency.

In this paper a method of recognizing waveform based on the Discrete Wavelet Transform (DWT) presented by us is applied to detecting the K-complex in human's EEG which is a slow wave overridden by fast rhythms (called as spindle). The features of K-complex are extracted in terms of three parameters: the local maxima of the wavelet transform modulus, average slope and the number of DWT coefficients in a wave. The 4th order B-spline wavelet is selected as the wavelet basis. Two channels at different resolutions are used to detect slow wave and sleep spindle contained in the K-complex. According to the principle of the minimum distance classification the classifiers are designed in order to decide the thresholds of recognition criteria. The EEG signal containing K-complexes elicited by sound stimuli is used as pattern to train the classifiers. Compared with traditional method of waveform recognition in time domain, this method has the advantage of automatically classifying duration ranks of various waves with different frequencies. Hence, it specially is suitable to recognition of signals which are the superimposition of waves with different frequencies. The experimental results of detection of K-complexes indicate that the method is effective.

A new method for the compression of electrocardiographic (ECG) data is presented. The method is based on the orthonormal wavelet analysis recently developed in applied mathematics. By using wavelet transform, the original signal is decomposed into a set of sub-signals with different frequency channels corresponding to the different physical features of the signal. By utilizing the optimum bit allocation scheme, each decomposed sub-signal is treated according to its contribution to the total reconstruction distortion and to the bit rate. In our experiments, compression ratios (CR) from 13.5: 1 to 22.9: 1 with the corresponding percent rms difference (PRD) between 5.5% and 13.3% have been obtained at a clinically acceptable signal quality. Experimental results show that the proposed method seems suitable for the compression of ECG data in the sense of high compression ratio and high speed.

MultiWave data compression algorithm is based on the multiresolution wavelet techniqu for decomposing Electrocardiogram (ECG) signals into their coarse and successively more detailed components. At each successive resolution, or scale, the data are convolved with appropriate filters and then the alternate samples are discarded. This procedure results in a data compression rate that increased on a dyadic scale with successive wavelet resolutions. ECG signals recorded from patients with normal sinus rhythm, supraventricular tachycardia, and ventriular tachycardia are analyzed. The data compression rates and the percentage distortion levels at each resolution are obtained. The performance of the MultiWave data compression algorithm is shown to be superior to another algorithm (the Turning Point algorithm) that also carries out data reduction on a dyadic scale.

A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks presented with respect to a family of n-dimensional signals which are not necessarily band-limited. It is assumed that the Fourier spectrums of these signals have weighted L2 norms smaller than a given positive number. In this paper, we establish a theory that the presented optimum interpolation functions satisfy the generalized discrete orthogonality and minimize the wide variety of measures of error simultaneously. In the following discussion, we assume initially that the corresponding approximation formula uses the infinite number of interpolation functions having limited supports and functional forms different from each other. However, it should be noted that the resultant optimum interpolation functions can be realized as the parallel shift of the finite number of space-limited functions. Some remarks to the problem of distinction of images is presented relating to the generalized discrete orthogonality and the reciprocal property for the proposed approximation.

A new method by which images are coded with predictable and controllable subjective picture quality in the minimum cost of bit rate is developed. By using wavelet transform, the original image is decomposed into a set of subimages with different frequency channels and resolutions. By utilizing human contrast sensitivity, each decomposed subimage is treated according to its contribution to the total visual quality and to the bit rate. A relationship between physical errors (mainly quantization errors) incurred in the orthonormal wavelet image coding system and the subjective picture quality quantified as the mean opinion score (MOS) is established. Instred of using the traditional optimum bit allocation scheme which minimizes a distortion cost function under the constraint of a given bit rate, we develop an "optimum visually weighted noise power allocation" (OVNA) scheme which emphasizes the satisfying of a desired subjective picture quality in the minumum cost of bit rate. The proposed method enables us to predict and control the picture quality before the reconstruction and to compress images with desired subjective picture quality in the minimum bit rate.

A complete analysis for the quantization noises and the reconstruction noises of the wavelet pyramid coding system is given. It is shown that in the (orthonormal) wavelet image coding system, there exists a simple and exact formula to compute the reconstruction mean-square-error (MSE) for any kind of quantization errors. Based on the noise analysis, an optimal bit allocation scheme which minimizes the system reconstruction distortion at a given rate is developed. The reconstruction distortion of a wavelet pyramid system is proved to be directly proportional to 2-2, where is a given bit rate. It is shown that, when the optimal bit allocation scheme is adopted, the reconstruction noises can be approximated to white noises. Particularly, it is shown that with only one known quantization MSE of a wavelet decomposition at any layer of the wavelet pyramid, all of the reconstruction MSE's and the quantization MSE's of the coding system can be easily calculated. When uniform quantizers are used, it is shown that at two successive layers of the wavelet pyramid, the optimal quantization step size is a half of its predecessor, which coincides with the resolution version of the wavelet pyramid decomposition. A comparison between wavelet-based image coding and some well-known traditional image coding methods is made by simulations, and the reasons why the wavelet-based image coding is superior to the traditional image coding are explained.