Michael L. Hilton

Wavelet and wavelet packet compression of electrocardiograms

Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECGs by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECGs are clinically useful.

Compressing still and moving images with wavelets

The wavelet transform has become a cutting-edge technology in image compression research. This article explains what wavelets are and provides a practical, nuts-and-bolts tutorial on wavelet-based compression that will help readers to understand and experiment with this important new technology.

Local enhancement of compressed images

We develop a simple focusing technique for wavelet decompositions. This allows us to single out interesting parts of an image and obtain variable compression rates over the image. We also study similar techniques for image enhancement.

Computationally fast wavelet-based video coding scheme

We present a new technique for rapidly evaluating the inverse wavelet transform in video compression applications. The wavelet transform decomposes each pixel in an image into a linear combination of basis functions. Typically, very few pixels in a video sequence change from one image to the next; therefore, very few of the coefficients in the transformed video sequence change from one image to the next. We capitalize on this fact, and speed up the reconstruction of transformed image sequences by computing the inverse transform for only those coefficients that have changed since the previous image. Our prototype software-only video decompressor based on this idea is capable of reconstructing 256 by 256, 8-bits per pixel, greyscale images at a rate of 18 frames per second at a compression ratio of about 22:1.

Distributed multisensor integration in a cooperative multirobot system

A trend is emerging, as detailed by McKee, towards the use of networks of smaller distributed robots for complicated tasks. A number of areas need to be addressed before such systems can be put into practical environments. Among these are the transfer and sharing of information between robots, control strategies for sensing and movement, interfaces for teleoperator assistance to the multirobot systems, and degree of autonomy. This paper presents a cooperative multirobot system framework that has a flexible degree of autonomy, depending on the complexity of the task that is to be performed. The system uses a wavelet-based method to address the pose and orientation calculations for robot positioning. Our previous work in this area demonstrated that reasonable sensor integration can be done within the wavelet domain at the coarse level. Augmented finite state machines are used under a subsumption architecture for control and integration of local and global maps for the multirobot system. This allows us to explicitly include the teleoperator interface in the system design. We also present the results of an experimental simulation study of a spinning satellite retrieval by three cooperating robots. This simulation includes full orbital dynamics effects such as atmospheric drag and non-spherical gravitation field perturbations.

Multiplicative and zero-crossing representations of signals

The implicit sampling theorem of Bar-David gives a representation of band limited functions using their crossings with a cosine function. This cosine function is chosen such that its difference with the original function has sufficient zero crossings for a unique representation. We show how, on an interval, this leads to a multiplicative representation involving a Riesz product. This provides an alternative to the classic additive Fourier series. We discuss stability and implementation issues. Since we have an explicit reconstruction formula, there is no need for an iterative algorithm.

Region-based wavelet image compression

Transform-based image coders exploit the information packing ability of some mathematical transforms in order to reduce the number of significant transform coefficients needed to accurately represent an image. Large coefficients are often associated with those regions where an image changes a lot, such as the boundaries between objects with differing visual characteristics. One way to reduce the number of significant transform coefficients is to segment an image into regions of similarity and then apply the transform to each region separately. We propose a novel image compression technique which first segments an image into arbitrary regions and then applies a region-adapted wavelet transform to each region.

Wavelet-based cosine crossings of signals

The periodic Bar-David (1974) sampling theorem provides an implicit representation of band limited signals using their crossings with a cosine function to form a multiplicative representation involving a Riesz product. The cosine crossings form a unique and stable representation of the signal. We incorporate the wavelet transform into the cosine crossing representation and show that they may be used to compactly represent overcomplete signal expansions.

Image representation based on cosine crossings of wavelet decompositions

The sampling theorem of Bar-David provides an implicit representation of bandlimited signals using their crossings with a cosine function. This cosine function is chosen in a way that guarantees a unique representation of the signal. Previously, we extended Bar-Davids theorem to periodic functions on an interval, leading to a multiplicative representation involving a Riesz product whose roots form a unique and stable representation of the signal. We also presented numerical algorithms for the analysis and synthesis of 1D signals. In this paper, we extend our previous results by developing algorithms for 2D signals and incorporating the wavelet transform into the cosine crossing representation.

Audio compression based on sine‐crossing representations of signals

The sampling theorem of Bar‐David [J. Bar‐David, Info. Control 24, 36–44 (1974)] provides an implicit representation of bandlimited signals using their crossings with a sine function. This sine function is chosen in a way that guarantees a unique representation of the signal. On a finite signal, this leads to a multiplicative representation involving a Riesz product whose roots form the representation of the original signal. These roots can be encoded to provide high‐quality, near lossless audio compression. The sine crossing representation can also be combined with the wavelet transform to provide further compression. [Work supported by ONR.]