"Rewiring" Filterbanks for Local Fourier Analysis: Theory and Practice

This article describes a series of new results outlining equivalences between certain "rewirings" of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to a general framework of reverse-order and convolution subband structures in filterbank transforms, which we show to be well suited to the analysis of filterbank coefficients arising from subsampled or multiplexed signals. These results thus provide a means to understand time-localized aliasing and modulation properties of such signals and their subband representations--notions that are notably absent from the global viewpoint afforded by Fourier analysis. The utility of filterbank rewirings is demonstrated by the closed-form analysis of signals subject to degradations such as missing data, spatially or temporally multiplexed data acquisition, or signal-dependent noise, such as are often encountered in practical signal processing applications

Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data

The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. In this article, we first show how the so-called Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. We then provide two main theorems on Skellam shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting and the other providing for unbiased risk estimation in a frequentist context. These results serve to yield new estimators in the Haar transform domain, including an unbiased risk estimate for shrinkage of Haar-Fisz variance-stabilized data, along with accompanying low-complexity algorithms for inference. We conclude with a simulation study demonstrating the efficacy of our Skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature, confirming that they offer substantial performance improvements over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for publicatio

Femtosecond Demagnetization and Hot Hole Relaxation in Ferromagnetic GaMnAs

We have studied ultrafast photoinduced demagnetization in GaMnAs via two-color time-resolved magneto-optical Kerr spectroscopy. Below-bandgap midinfrared pump pulses strongly excite the valence band, while near-infrared probe pulses reveal sub-picosecond demagnetization that is followed by an ultrafast ($\sim$1 ps) partial recovery of the Kerr signal. Through comparison with InMnAs, we attribute the signal recovery to an ultrafast energy relaxation of holes. We propose that the dynamical polarization of holes through $p$-$d$ scattering is the source of the observed probe signal. These results support the physical picture of femtosecond demagnetization proposed earlier for InMnAs, identifying the critical roles of both energy and spin relaxation of hot holes.Comment: 7 pages, 6 figure

Spatio-Spectral Sampling and Color Filter Array Design

Owing to the growing ubiquity of digital image acquisition and display, several factors must be considered when developing systems to meet future color image processing needs, including improved quality, increased throughput, and greater cost-effectiveness. In consumer still-camera and video applications, color images are typically obtained via a spatial subsampling procedure implemented as a color filter array (CFA), a physical construction whereby only a single component of the color space is measured at each pixel location. Substantial work in both industry and academia has been dedicated to post-processing this acquired raw image data as part of the so-called image processing pipeline, including in particular the canonical demosaicking task of reconstructing a full-color image from the spatially subsampled and incomplete data acquired using a CFA. However, as we detail in this chapter, the inherent shortcomings of contemporary CFA designs mean that subsequent processing steps often yield diminishing returns in terms of image quality. For example, though distortion may be masked to some extent by motion blur and compression, the loss of image quality resulting from all but the most computationally expensive state-of-the-art methods is unambiguously apparent to the practiced eye. … As the CFA represents one of the first steps in the image acquisition pipeline, it largely determines the maximal resolution and computational efficiencies achievable by subsequent processing schemes. Here, we show that the attainable spatial resolution yielded by a particular choice of CFA is quantifiable and propose new CFA designs to maximize it. In contrast to the majority of the demosaicking literature, we explicitly consider the interplay between CFA design and properties of typical image data and its implications for spatial reconstruction quality. Formally, we pose the CFA design problem as simultaneously maximizing the allowable spatio-spectral support of luminance and chrominance channels, subject to a partitioning requirement in the Fourier representation of the sensor data. This classical aliasing-free condition preserves the integrity of the color image data and thereby guarantees exact reconstruction when demosaicking is implemented as demodulation (demultiplexing in frequency)

Ontology for Data Representation in the Production of Cotton Fiber in Brazil

An important feature in computer systems developed for the agricultural sector is to satisfy the heterogeneity of data generated in different processes. Most problems related with this heterogeneity arise from the lack of standard for different computing solutions proposed. An efficient solution for that is to create a single standard for data exchange. The study on the actual process involved in cotton production was based on a research developed by the Brazilian Agricultural Research Corporation (EMBRAPA) that reports all phases as a result of the compilation of several theoretical and practical researches related to cotton crop. The proposition of a standard starts with the identification of the most important classes of data involved in the process, and includes an ontology that is the systematization of concepts related to the production of cotton fiber and results in a set of classes, relations, functions and instances. The results are used as a reference for the development of computational tools, transforming implicit knowledge into applications that support the knowledge described. This research is based on data from the Midwest of Brazil. The choice of the cotton process as a study case comes from the fact that Brazil is one of the major players and there are several improvements required for system integration in this segment

Mechanism of carrier-induced ferromagnetism in magnetic semiconductors

Taking into account both random impurity distribution and thermal fluctuations of localized spins, we have performed a model calculation for the carrier (hole) state in Ga$_{1-x}$Mn$_x$As by using the coherent potential approximation (CPA). The result reveals that a {\it p}-hole in the band tail of Ga$_{1-x}$Mn$_x$As is not like a free carrier but is rather virtually bounded to impurity sites. The carrier spin strongly couples to the localized {\it d} spins on Mn ions. The hopping of the carrier among Mn sites causes the ferromagnetic ordering of the localized spins through the double-exchange mechanism. The Curie temperature obtained by using conventional parameters agrees well with the experimental result.Comment: 7 pages, 4 figure

Ultrafast demagnetization in the sp-d model: a theoretical study

We propose and analyze a theoretical model of ultrafast light-induced magnetization dynamics in systems of localized spins that are coupled to carriers' spins by sp-d exchange interaction. A prominent example of a class of materials falling into this category are ferromagnetic (III,Mn)V semiconductors, in which ultrafast demagnetization has been recently observed. In the proposed model light excitation heats up the population of carriers, taking it out of equilibrium with the localized spins. This triggers the process of energy and angular momentum exchange between the two spin systems, which lasts for the duration of the energy relaxation of the carriers. We derive the Master equation for the density matrix of a localized spin interacting with the hot carriers and couple it with a phenomenological treatment of the carrier dynamics. We develop a general theory within the sp-d model and we apply it to the ferromagnetic semiconductors, taking into account the valence band structure of these materials. We show that the fast spin relaxation of the carriers can sustain the flow of polarization between the localized and itinerant spins leading to significant demagnetization of the localized spin system, observed in (III,Mn)V materials.Comment: 15 pages, 8 figure

Spin dynamics of a one-dimensional spin-1/2 fully anisotropic Ising-like antiferromagnet in a transverse magnetic field

We consider the one-dimensional Ising-like fully anisotropic S=1/2 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in the presence of transverse magnetic field $h_x$. We obtain dynamical spin correlation functions along the magnetic field $S^{xx}(q,\omega)$ and perpendicular to it $S^{yy}(q,\omega)$. It is shown that the line shapes of $S^{xx}(q,\omega)$ and $S^{yy}(q,\omega)$ are purely symmetric at the zone-boundary. It is observed in $S^{yy}(q,\omega)$ for $\pi/2<q<\pi$ that the spectral weight moves toward low energy side with the increase of $h_x$. This model is applicable to study the spin dynamics of CsCoCl$_3$ in the presence of weak interchain interactions.Comment: 19 pages, LaTeX, 12 eps figure

Presentations of major peripheral arterial disease and risk of major outcomes in patients with type 2 diabetes: results from the ADVANCE-ON study.

BACKGROUND: Peripheral arterial disease (PAD) is known to be associated with high cardiovascular risk, but the individual impact of PAD presentations on risk of macrovascular and microvascular events has not been reliably compared in patients with type 2 diabetes. We aimed to evaluate the impact of major PAD, and its different presentations, on the 10-year risk of death, major macrovascular events, and major clinical microvascular events in these patients. METHODS: Participants in the action in diabetes and vascular disease: PreterAx and DiamicroN modified-release controlled evaluation (ADVANCE) trial and the ADVANCE-ON post-trial study were followed for a median of 5.0 (in-trial), 5.4 (post-trial), and 9.9 (overall) years. Major PAD at baseline was subdivided into lower-extremity chronic ulceration or amputation secondary to vascular disease and history of peripheral revascularization by angioplasty or surgery. RESULTS: Among 11,140 participants, 516 (4.6 %) had major PAD at baseline: 300 (2.7 %) had lower-extremity ulceration or amputation alone, 190 (1.7 %) had peripheral revascularization alone, and 26 (0.2 %) had both presentations. All-cause mortality, major macrovascular events, and major clinical microvascular events occurred in 2265 (20.3 %), 2166 (19.4 %), and 807 (7.2 %) participants, respectively. Compared to those without PAD, patients with major PAD had increased rates of all-cause mortality (HR 1.35, 95 % CI 1.15-1.60, p = 0.0004), and major macrovascular events (1.47 [1.23-1.75], p < 0.0001), after multiple adjustments for region of origin, cardiovascular risk factors and treatments, peripheral neuropathy markers, and randomized treatments. We have also observed a trend toward an association of baseline PAD with risk of major clinical microvascular events [1.31 (0.96-1.78), p = 0.09]. These associations were comparable for patients with a lower-extremity ulceration or amputation and for those with a history of peripheral revascularization. Furthermore, the risk of retinal photocoagulation or blindness, but not renal events, increased in patients with lower-extremity ulceration or amputation [1.53 (1.01-2.30), p = 0.04]. CONCLUSIONS: Lower-extremity ulceration or amputation, and peripheral revascularization both increased the risks of death and cardiovascular events, but only lower-extremity ulceration or amputation increased the risk of severe retinopathy in patients with type 2 diabetes. Screening for major PAD and its management remain crucial for cardiovascular prevention in patients with type 2 diabetes (ClinicalTrials.gov number, NCT00949286)