David K Hammond

• Ph. D.
• Professor (Assistant) at Oregon Institute of Technology

We describe the discrete Laplacian deconvolution (DLD) method for reconstructing an image from its directional derivatives in multiple directions. The DLD models the derivative measurements as discrete convolutions and efficiently computes the ridge regression or the pseudoinverse estimate of the underlying image using the fast Fourier transform. W...

The spectral graph wavelet transform (SGWT) defines wavelet transforms appropriate for data defined on the vertices of a weighted graph. Weighted graphs provide an extremely flexible way to model the data domain for a large number of important applications (such as data defined on vertices of social networks, transportation networks, brain connecti...

Rationale Accurate cortical source estimation from magneto- and electroencephalography (MEG/EEG) ideally relies on subject specific forward head models that enable computation of lead fields to the scalp. With the widespread use of MRI and CT availability anatomically realistic head models can be used routinely, however there is still a lack of age...

We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal n by n matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. For large n, we show there are up to 4 eigenvalues, the so-called special eigenvalues, whose behavior depends sensitively on the bo...

We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary conditions, we mean the first and last row of the matrix. For large $n$, we show there are up to $4$ eigenvalues,...

It is a poster presented at OHBM 2017

With changes to carbon output imminent as a result of governmental policies, the method by which energy generators in competitive markets are selected for operation can be called into question. We first simulated a bid-based day-ahead market with human participants and then analyzed generation asset owners’ profits based on bid strategy. We then st...

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. After describing necessary and sufficient conditions for asymptotic s...

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a...

In this document we introduce a Matlab toolbox called the Graph Signal Processing toolbox (GSPBox). This toolbox is based on spectral graph theory, more specifically graph filtering. It includes fast filtering routines using Chebychev polynomials as presented in [4]. This document is automatically generated from the source files and includes the co...

We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flo...

We propose a novel difference metric, called the graph diffusion distance (GDD), for quantifying the difference between two weighted graphs with the same number of vertices. Our approach is based on measuring the average similarity of heat diffusion on each graph. We compute the graph Laplacian exponential kernel matrices, corresponding to repeated...

The EEG source estimation problem consists of inferring cortical activation from measurements of electrical potential taken on the scalp surface. This inverse problem is intrinsically ill-posed. In particular the dimensionality of cortical sources greatly exceeds the number of electrode measurements, and source estimation requires regularization to...

This paper studies the problem of reconstructing sparse or compressible signals from compressed sensing measurements that have undergone nonuniform quantization. Previous approaches to this Quantized Compressed Sensing (QCS) problem based on Gaussian models (bounded l2-norm) for the quantization distortion yield results that, while often acceptable...

The source estimation problem for EEG consists of estimating cortical activity from measurements of electrical potential on the scalp surface. This is a underconstrained inverse problem as the dimensionality of cortical source currents far exceeds the number of sensors. We develop a novel regularization for this inverse prob-lem which incorporates...

Following the Compressed Sensing (CS) paradigm, this paper studies the problem of recovering sparse or compressible signals from (scalar) non-uniformly quantized measurements. We show that a simple adaptation of the Basis Pursuit De-Quantizer introduced earlier, that is, a sign sensitive weighting of their ℓp-norm fidelity constraint, yields good S...

In this paper, we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment p (BPDQ_p), that model the quantization distortion more faithfully than the commonly used Basis Pursuit DeNo...

Understanding the milliscale (temporal and spatial) dynamics of the human brain activity requires high-resolution modeling of head electromagnetics and source localization of EEG data. We have developed an automated environment to construct individualized computational head models from image segmentation and to estimate conductivity parameters usin...

Understanding the milliscale (temporal and spatial) dynamics of the human brain activity requires high-resolution modeling of head electromagnetics and source localization of EEG data. We have developed an automated environment to construct individualized computational head models from image segmentation and to estimate conductivity parameters usin...

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L. Given a wavelet generating kernel g and a scale param...

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian $\L$. Given a wavelet generating kernel $g$ and a sc...

In this paper, following the Compressed Sensing (CS) paradigm, we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment p (BPDQ_p), that model the quantization distortion more fait...

In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$ (BPDQ$_p$), that model the quantization distortion more faithfully than the commonly used Basis Pursuit DeNoise (BP...

We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multiscale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated according to the values of two hidden random variables, thus allowing the model to adapt to the...

An algorithm is proposed for denoising the signal induced by cosmic strings in the cosmic microwave background (CMB). A Bayesian approach is taken, based on modeling the string signal in the wavelet domain with generalized Gaussian distributions. Good performance of the algorithm is demonstrated by simulated experiments at arcminute resolution unde...

Digital photographs are not random collections of pixels, but have strong structural and statistical regularity. Understanding the properties of natural image signals allows the development of better algorithms for image processing applications. One important property of natural images is the presence of strongly oriented features. In this thesis,...

We present a general framework for combination of two distinct local denoising methods. Interpolation between the two methods is controlled by a spatially varying decision function. Assuming the availability of clean training data, we formulate a learning problem for determining the decision function. As an example application we use Weighted Kerne...

We develop a statistical model for images that explicitly captures variations in local orientation and contrast. Patches of wavelet coefficients are described as samples of a fixed Gaussian process that are rotated and scaled according to a set of hidden variables representing the local image contrast and orientation. An optimal Bayesian least squa...

We present a nonlinear image representation based on multiscale local orientation measurements. Specifically, an image is first decomposed using a two-orientation steerable pyramid, a tight-frame representation in which the basis functions are directional derivatives of a radially symmetric blur-ring operator. The pair of subbands at each scale are...

In this talk, we discuss the issue of source separation in a signal on the sphere or on the plane, relying on the sparsity of one signal component in a scale-discretized steerable wavelet basis. The steerability of wavelets allows to probe in detail the local morphology of a signal at each analysis scale. It gives access to local measures of signed...