Sparse Correlation Kernel Analysis and Reconstruction

This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class- specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use Support Vector Machine (SVM) regression and compare this to traditional Principal Component Analysis (PCA) for the tasks of signal reconstruction, superresolution, and compression. The testbed we use in this paper is a set of images of pedestrians. This paper also presents results of experiments in which we use a dictionary of multiscale basis functions and then use Basis Pursuit De-Noising to obtain a sparse, multiscale approximation of a signal. The results are analyzed and we conclude that 1) when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction and superresolution, 2) for image compression, PCA and SVM have different tradeoffs, depending on the particular metric that is used to evaluate the results, 3) in sparse representation techniques, L_1 is not a good proxy for the true measure of sparsity, L_0, and 4) the L_epsilon norm may be a better error metric for image reconstruction and compression than the L_2 norm, though the exact psychophysical metric should take into account high order structure in images.

A Circuit Grammar For Operational Amplifier Design

Electrical circuit designers seldom create really new topologies or use old ones in a novel way. Most designs are known combinations of common configurations tailored for the particular problem at hand. In this thesis I show that much of the behavior of a designer engaged in such ordinary design can be modelled by a clearly defined computational mechanism executing a set of stylized rules. Each of my rules embodies a particular piece of the designer's knowledge. A circuit is represented as a hierarchy of abstract objects, each of which is composed of other objects. The leaves of this tree represent the physical devices from which physical circuits are fabricated. By analogy with context-free languages, a class of circuits is generated by a phrase-structure grammar of which each rule describes how one type of abstract object can be expanded into a combination of more concrete parts. Circuits are designed by first postulating an abstract object which meets the particular design requirements. This object is then expanded into a concrete circuit by successive refinement using rules of my grammar. There are in general many rules which can be used to expand a given abstract component. Analysis must be done at each level of the expansion to constrain the search to a reasonable set. Thus the rule of my circuit grammar provide constraints which allow the approximate qualitative analysis of partially instantiated circuits. Later, more careful analysis in terms of more concrete components may lead to the rejection of a line of expansion which at first looked promising. I provide special failure rules to direct the repair in this case.