In this paper, a speed and power-efficient set partitioning in hierarchical trees (SPIHT) design is introduced for one-dimensional (1-D) wavelet-based electrocardiography (ECG) compression systems with quality guarantee. To achieve real-time and low-power design objectives toward wearable quality-on-demand (QoD) ECG applications, we first propose a coding-time- and computation-efficient SPIHT algorithm using various types of coding status register files to overcome the disadvantages of low coding speeds and complicated hardware architectures characterizing prior SPIHT algorithms resulting from the necessity of dynamic computation and arrangement in the sorting and refinement processing phase. Second, a highly pipelined and power-efficient very large scale integration (VLSI) architecture is developed to implement a high-performance and low-power SPIHT design based on the proposed algorithm. The final simulation results demonstrate that our proposed algorithm can speed up the average coding time 1.52 to 2.74 times compared to prior work with an identical compression ratio for an 11-level $1024\times 1\,1-{\rm{D}}$ discrete wavelet transform at diverse target percentage root-mean-square differences (PRDT) on various MIT-BIH arrhythmia datasets. Applied to wearable wavelet-based QoD ECG applications, our proposed VLSI architecture attains a working frequency of 740 MHz and consumes an average of $\text{23}\ \mu {\text{W}}$ of power with Taiwan Semiconductor Manufacturing Company 90-nm CMOS technology, which shows the effectiveness of speed and power over the state-of-the-art designs.

A modified two-dimensional (2-D) discrete periodized wavelet transform (DPWT) based on the homeomorphic high-pass filter and the 2-D operator correlation algorithm is developed in this paper. The advantages of this modified 2-D DPWT are that it can reduce the multiplication counts and the complexity of boundary data processing in comparison to other conventional 2-D DPWT for perfect reconstruction. In addition, a parallel-pipeline architecture of the nonseparable computation algorithm is also proposed to implement this modified 2-D DPWT. This architecture has properties of noninterleaving input data, short bus width request, and short latency. The analysis of the finite precision performance shows that nearly half of the bit length can be saved by using this nonseparable computation algorithm. The operation of the boundary data processing is also described in detail. In the three-stage decomposition of an N/spl times/N image, the latency is found to be N/sup 2/+2N+18.

In the problem of specifying a well-defined wavelet description of a planar closed curve, defining a unique start point on the curve is crucial for wavelet representation. In this paper, a generalized uniqueness property inherent in the one-dimensional (1-D) discrete periodized wavelet transformation (DPWT) is derived. The uniqueness property facilitates a quantitative analysis of the one-to-one mapping between the variation of 1-D DPWT coefficients and the starting point shift of the originally sampled curve data. By employing the uniqueness property, a new shape descriptor called the uniqueness wavelet descriptor (UWD) by which the starting point is fixed entirely within the context of the wavelet representation is proposed. The robustness of the UWD against input noise is analyzed. On the basis of local shape characteristic enhancement, several experiments were conducted to illustrate the adaptability property of the UWD for desirable starting point determination. Our experiments of pattern recognition show that the UWD can provide a supervised pattern classifier with optimal features to obtain the best matching performance in the presence of heavy noise. In addition, the generalized uniqueness property can be used for the shape regularity measurement. The UWD does not have local support and therefore it can not be applied to contour segments.

This paper presents a fast algorithm to perform the 2-D discrete periodized wavelet transform based on the operator correlation algorithm (OCA). The OCA-based algorithm needs half of the multiplications and bits required by the classical algorithm. The OCA-based algorithm is modular inherent. It can be easily mapped to VLSI design.

The theorem of the generalized uniqueness property inherent in the 1-D discrete periodized wavelet transform (DPWT) is developed in this paper. The uniqueness property facilitates a quantitative analysis of the one-to-one mapping between the variation of 1-D DPWT coefficients and the starting point shift of the originally sampled curve data. By employing the uniqueness property, a new shape descriptor called the generalized uniqueness wavelet descriptor (GUWD) by which the starting point is fixed entirely within the context of the wavelet representation is proposed. The existence theorem of the GUWD supports the availability of the wavelet descriptor for pattern recognition and can provide an effective method to solve the problem of starting point dependency in the wavelet-based applications. In addition, the generalized uniqueness property can be used for shape regularity measurement.

Previously, the authors proposed an inverse-free Berlekamp-Massey (1968, 1969) algorithm to simplify the Reed-Solomon (RS) codes. This modified RS decoding method is the best known technique for finding the error locator polynomial. The inverse-free method is generalized to find both errors and erasures. The basic idea of the new procedure is the replacement of the initial condition of the BM algorithm by the Forney (1965) syndromes. With this improved technique, the complexity of time-domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches.

In this paper, the projection location constraint is exploited to reduce ambiguous correspondences in trinocular systems. The inherent matching problems associated with the spurious features produced by overlapping among targets, the periodic structure of objects and the occlusion features were solved. The projection location constraint can be achieved by the deviation-to-distance transformation and the optimal epipolar constraint. The deviation-to-distance transformation transforms the location deviation of the extracted feature on an image plane to a maximum distance between the potential corresponding features and the epipolar line on another image for restricting the searching area of correspondences. The optimal epipolar constraint is obtained by adjusting the camera model before systems start to work. With the deviation-to-distance transformation and the optimal epipolar constraint, the arbitral area for searching the potential corresponding features can be made reasonably small. This not only saves computational time but also results in fewer ambiguous correspondences. In practice, the importance of the paper is that it proposes a very easy adjustment of camera geometry to simplify the most troublesome matching problem encountered in stereo systems. All the discussions and derivations are based on the geometry of the camera model and the mapping between the locations of the 3D features and their projection locations on the image planes. The non-ambiguity probability of the trinocular system is derived theoretically and verified by experimental results.>