Digital Coding of Waveforms

The problem of signal representation in terms of basis vectors from a large, over-complete, spanning dictionary has been the focus of much research. Achieving a succinct, or 'sparse', representation is known as the problem of best basis representation. Methods are considered which seek to solve this problem by sequentially building up a basis set for the signal. Three distinct algorithm types have appeared in the literature which are here termed basic matching pursuit (BMP), order recursive matching pursuit (ORMP) and modified matching pursuit (MMP). The algorithms are first described and then their computation is closely examined. Modifications are made to each of the procedures which improve their computational efficiency. The complexity of each algorithm is considered in two contexts; one where the dictionary is variable (time-dependent) and the other where the dictionary is fixed (time-independent). Experimental results are presented which demonstrate that the ORMP method is the best procedure in terms of its ability to give the most compact signal representation, followed by MMP and then BMP which gives the poorest results. Finally, weighing the performance of each algorithm, its computational complexity and the type of dictionary available, recommendations are made as to which algorithm should be used for a given problem.

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Forward sequential algorithms for best basis selection

List of Figures. Foreword M. Vetterli. Preface. 1. Signal Models and Analysis-Synthesis. 2. Sinusoidal Modeling. 3. Multiresolution Sinusoidal Modeling. 4. Residual Modeling. 5. Pitch-Synchronous Models. 6. Matching Pursuit and Atomic Models. 7. Conclusions. Appendix A: Two-Channel Filter Banks. Appendix B: Fourier Series Representations. References. References for Poetry Excerpts. Index.

Adaptive Signal Models: Theory, Algorithms, and Audio Applications

At low bit rates, better coding quality can be achieved by downsampling the image prior to compression and estimating the missing portion after decompression. This paper presents a new algorithm in such a paradigm, based on the adaptive decision of appropriate downsampling directions/ratios and quantization steps, in order to achieve higher coding quality with low bit rates with the consideration of local visual significance. The full-resolution image can be restored from the DCT coefficients of the downsampled pixels so that the spatial interpolation required otherwise is avoided. The proposed algorithm significantly raises the critical bit rate to approximately 1.2 bpp, from 0.15-0.41 bpp in the existing downsample-prior-to-JPEG schemes and, therefore, outperforms the standard JPEG method in a much wider bit-rate scope. The experiments have demonstrated better PSNR improvement over the existing techniques before the critical bit rate. In addition, the adaptive mode decision not only makes the critical bit rate less image-independent, but also automates the switching coders in variable bit-rate applications, since the algorithm turns to the standard JPEG method whenever it is necessary at higher bit rates

Adaptive downsampling to improve image compression at low bit rates

Most current image retrieval systems and commercial search engines use mainly text annotations to index and retrieve WWW images. This research explores the use of machine learning approaches to automatically annotate WWW images based on a predefined list of concepts by fusing evidences from image contents and their associated HTML text. One major practical limitation of employing supervised machine learning approaches is that for effective learning, a large set of labeled training samples is needed. This is tedious and severely impedes the practical development of effective search techniques for WWW images, which are dynamic and fast-changing. As web-based images possess both intrinsic visual contents and text annotations, they provide a strong basis to bootstrap the learning process by adopting a co-training approach involving classifiers based on two orthogonal set of features -- visual and text. The idea of co-training is to start from a small set of labeled training samples, and successively annotate a larger set of unlabeled samples using the two orthogonal classifiers. We carry out experiments using a set of over 5,000 images acquired from the Web. We explore the use of different combinations of HTML text and visual representations. We find that our bootstrapping approach can achieve a performance comparable to that of the supervised learning approach with an F1 measure of over 54%. At the same time, it offers the added advantage of requiring only a small initial set of training samples.

A bootstrapping framework for annotating and retrieving WWW images

This paper presents two multiresolution segmentation-based algorithms for low bit rate image compression using hierarchical data structures. The segmentation is achieved with quadtree and binary space partitioning tree hierarchical data structures and the encoding is performed by using the projection pursuit (matching pursuit) with a finite dictionary of spline functions with various degrees of smoothness. Comparison with JPEG at rates below 0.5 bit/pixel shows superior performance both in terms of peak signal-to-noise ratio (PSNR) and subjective image quality.

Multiresolution segmentation-based image coding with hierarchical data structures

A novel multiresolution algorithm for lossy gray-scale image compression is presented High-quality low bit rate image compression is achieved first by segmenting an image into regions of different sizes based on perceptual variation in each region and then constructing a distinct code for each block by using the theory of projection pursuit (PP) Projection pursuit allows one to adaptively construct a better approximation for each block by optimally selecting basis functions The process is stopped when the desired peak signal-to-noise ratio (PSNR) or bit rate (b/pixel) is achieved At rates below 05 b/pixel, our algorithm shows superior performance, both in terms of PSNR and subjective image quality, over the Joint Photographers Expert Group (JPEG) algorithm, and comparable performance to the embedded zerotree wavelet (EZW) algorithm

Projection pursuit image compression with variable block size segmentation

In this paper, a novel multiresolution algorithm for low bit-rate image compression is presented. High quality low bit-rate image compression is achieved by first decomposing the image into approximation and detail subimages with a shift-orthogonal multiresolution analysis. Then, at the coarsest resolution level, the coefficients of the transformation are encoded by an orthogonal matching pursuit algorithm with a wavelet packet dictionary. Our dictionary consists of convolutional splines of up to order two for the detail and approximation subbands. The intercorrelation between the various resolutions is then exploited by using the same bases from the dictionary to encode the coefficients of the finer resolution bands at the corresponding spatial locations. To further exploit the spatial correlation of the coefficients, the zero trees of wavelets (EZW) algorithm was used to identify the potential zero trees. The coefficients of the presentation are then quantized and arithmetic encoded at each resolution, and packed into a scalable bit stream structure. Our new algorithm is highly bit-rate scalable, and performs better than the segmentation based matching pursuit and EZW encoders at lower bit rates, based on subjective image quality and peak signal-to-noise ratio.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Low-bit-rate subband image coding with matching pursuits

In this paper, a novel algorithm for low bit-rate image compression is presented. In this technique, we use a new image representation algorithm called segmented orthogonal matching pursuit (SOMP) (Rabiee and Kashyap, 1998) to encode the subbands of an image. Our preliminary results show that our algorithm performs better than the segmentation based matching pursuit (QTMP) (Rabiee et al. 1996) and EZW (Shapiro 1993) encoders at lower bit rates, based on subjective image quality and peak signal-to-noise ratio (PSNR).

Scalable subband image coding with segmented orthogonal matching pursuit

There has been a growing interest in representation and compression of signals by using dictionaries of basis functions other than the traditional dictionary of sinusoids. These new set of dictionaries include cosine packets, chirplets, Gabor functions, wavelets, and wavelet packets. In this paper matching pursuit and basis pursuit with finite dictionaries of convolutional splines are used for adaptive multiresolution image compression. At the cost of computational complexity these algorithms outperform the DCT based JPEG both in terms of PSNR and subjective image quality at lower bit rates.

S.R. Safavian

Papers

Multiresolution segmentation-based image coding with hierarchical data structures

Projection pursuit image compression with variable block size segmentation

Low-bit-rate subband image coding with matching pursuits

Scalable subband image coding with segmented orthogonal matching pursuit

Adaptive multiresolution image coding with matching and basis pursuits