A binary wavelet decomposition of binary images.

We construct a theory of binary wavelet decompositions of finite binary images. The new binary wavelet transform uses simple module-2 operations. It shares many of the important characteristics of the real wavelet transform. In particular, it yields an output similar to the thresholded output of a real wavelet transform operating on the underlying binary image. We begin by introducing a new binary field transform to use as an alternative to the discrete Fourier transform over GF(2). The corresponding concept of sequence spectra over GF(2) is defined. Using this transform, a theory of binary wavelets is developed in terms of two-band perfect reconstruction filter banks in GF(2). By generalizing the corresponding real field constraints of bandwidth, vanishing moments, and spectral content in the filters, we construct a perfect reconstruction wavelet decomposition. We also demonstrate the potential use of the binary wavelet decomposition in lossless image coding.

An eigenstructure approach to edge detection.

A procedure for detecting step edges in noisy signals that does not involve any prefiltering of the data is proposed. It locates step edges in 1-D noisy signals as follows. First, it computes the eigenvectors corresponding to the three smallest eigenvalues of a matrix formed with the discrete Fourier transform of the given data. Next, it estimates the edge locations by finding the local minima in the sum of the spectra of the computed eigenvectors. The technique computes a point edge map for 2-D images by analyzing each row, column, and 45 degrees and 135 degrees diagonal in the image. The computational complexity of the proposed procedure is determined.

Arithmetic coding with dual symbol sets and its performance analysis.

In this paper, we propose a novel adaptive arithmetic coding method that uses dual symbol sets: a primary symbol set that contains all the symbols that are likely to occur in the near future and a secondary symbol set that contains all other symbols. The simplest implementation of our method assumes that symbols that have appeared in the previously are highly likely to appear in the near future. It therefore fills the primary set with symbols that have occurred in the previously. Symbols move dynamically between the two symbol sets to adapt to the local statistics of the symbol source. The proposed method works well for sources, such as images, that are characterized by large alphabets and alphabet distributions that are skewed and highly nonstationary. We analyze the performance of the proposed method and compare it to other arithmetic coding methods, both theoretically and experimentally. We show experimentally that in certain contexts, e.g., with a wavelet-based image coding scheme that has appeared in the literature, the compression performance of the proposed method is better than that of the conventional arithmetic coding method and the zero-frequency escape arithmetic coding method.

Subband domain coding of binary textual images for document archiving.

In this work, a subband domain textual image compression method is developed. The document image is first decomposed into subimages using binary subband decompositions. Next, the character locations in the subbands and the symbol library consisting of the character images are encoded. The method is suitable for keyword search in the compressed data. It is observed that very high compression ratios are obtained with this method. Simulation studies are presented.

Time delay estimation using wavelet transform for pulsed-wave ultrasound.

The windowed cross-correlation (WCC) technique has recently attracted attention in pulsed-wave (PW) ultrasound for measurement of tissue motion and blood flow velocity because of its performance advantages over the conventional Doppler method. The WCC measures tissue motion and blood flow velocity via estimation of time delays of backscattered signals in two consecutive echoes. In this paper, we propose a wavelet transform-based cross-correlation (WTCC) technique for the time delay estimation in PW ultrasound. The WTCC consists of three steps: (i) computing wavelet transforms (WTs) of received echoes, (ii) computing cross-correlations in the wavelet domain, and (iii) estimating the time delays by maximizing the estimated cross-correlations. Dyadic or continuous wavelets may be used in the proposed approach. The WTCC has a unique feature of using varying time-frequency windows in processing compared with the WCC which only uses a single fixed window. Our computer simulations show that, compared with the WCC, the WTCC provides a better estimation of time delays (lower failure rate and lower estimate error) and its performance is more consistent under various conditions, and more robust with window size. In the simulations, we also tested a specific continuous wavelet for the WTCC that was the emitted pulse itself and found the corresponding WTCC outperforms the WTCC with a regular dyadic wavelet.