Sampling systems matched to input processes and image classes

This dissertation investigates sampling and reconstruction of wide sense stationary (WSS) random processes from their sample random variables . In this context, two types of sampling systems are studied, namely, interpolation and approximation sampling systems. We aim to determine the properties of the filters in these systems that minimize the mean squared error between the input process and the process reconstructed from its samples. More specifically, for the interpolation sampling system we seek and obtain a closed form expression for an interpolation filter that is optimal in this sense. Likewise, for the approximation sampling system we derive a closed form expression for an optimal reconstruction filter given the statistics of the input process and the antialiasing filter. Using these expressions we show that Meyer-type scaling functions and wavelets arise naturally in the context of subsampled bandlimited processes. We also derive closed form expressions for the mean squared error incurred by both the sampling systems. Using the expression for mean squared error we show that for an approximation sampling system, minimum mean squared error is obtained when the antialiasing filter and the reconstruction filter are spectral factors of an ideal brickwall-type filter. Similar results are derived for the discrete-time equivalents of these sampling systems. Finally, we give examples of interpolation and approximation sampling filters and compare their performance with that of some standard filters. The implementation of these systems is based on a novel framework called the perfect reconstruction circular convolution (PRCC) filter bank framework. The results obtained for the one dimensional case are extended to the multidimensional case. Sampling a multidimensional random field or image class has a greater degree of freedom and the sampling lattice can be defined by a nonsingular matrix D. The aim is to find optimal filters in multidimensional sampling systems to reconstruct the input image class from its samples on a lattice defined by D. Closed form expressions for filters in multidimensional interpolation and approximation sampling systems are obtained as are expressions for the mean squared error incurred by each system. For the approximation sampling system it is proved that the antialiasing and reconstruction filters that minimize the mean squared error are spectral factors of an ideal brickwall-type filter whose support depends on the sampling matrix D. Finally. we give examples of filters in the interpolation and approximation sampling systems for an image class derived from a LANDSAT image and a quincunx sampling lattice. The performance of these filters is compared with that of some standard filters in the presence of a quantizer

An experimental course on digital communications

In this paper a laboratory course on digital communications is presented. This course has been designed for medium degree professionals in the telecommunications field, and it is based on training equipment developed to change the usual theoretical classrooms for laboratory seminars.Peer ReviewedPostprint (published version

Sampling from a system-theoretic viewpoint: Part I - Concepts and tools

This paper is first in a series of papers studying a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. In this paper we present the paradigm and revise underlying technical tools, such as the lifting technique and some topics of the operator theory. This material facilitates a systematic and unified treatment of a wide range of sampling and reconstruction problems, recovering many hitherto considered different solutions and leading to new results. Some of these applications are discussed in the second part

Spatiotemporal Antialiasing in Photoacoustic Computed Tomography

Photoacoustic computed tomography (PACT) based on a full-ring ultrasonic transducer array is widely used for small animal wholebody and human organ imaging, thanks to its high in-plane resolution and full-view fidelity. However, spatial aliasing in full-ring geometry PACT has not been studied in detail. If the spatial Nyquist criterion is not met, aliasing in spatial sampling causes artifacts in reconstructed images, even when the temporal Nyquist criterion has been satisfied. In this work, we clarified the source of spatial aliasing through spatiotemporal analysis. We demonstrated that the combination of spatial interpolation and temporal filtering can effectively mitigate artifacts caused by aliasing in either image reconstruction or spatial sampling, and we validated this method by both numerical simulations and in vivo experiments

Morphological Antialiasing and Topological Reconstruction

International audienceMorphological antialiasing is a post-processing approach which does note require additional samples computation. This algorithm acts as a non-linear filter, ill-suited to massively parallel hardware architectures. We redesigned the initial method using multiple passes with, in particular, a new approach to line length computation. We also introduce in the method the notion of topological reconstruction to correct the weaknesses of postprocessing antialiasing techniques. Our method runs as a pure post-process filter providing full-image antialiasing at high framerates, competing with traditional MSAA

k-d Darts: Sampling by k-Dimensional Flat Searches

We formalize the notion of sampling a function using k-d darts. A k-d dart is a set of independent, mutually orthogonal, k-dimensional subspaces called k-d flats. Each dart has d choose k flats, aligned with the coordinate axes for efficiency. We show that k-d darts are useful for exploring a function's properties, such as estimating its integral, or finding an exemplar above a threshold. We describe a recipe for converting an algorithm from point sampling to k-d dart sampling, assuming the function can be evaluated along a k-d flat. We demonstrate that k-d darts are more efficient than point-wise samples in high dimensions, depending on the characteristics of the sampling domain: e.g. the subregion of interest has small volume and evaluating the function along a flat is not too expensive. We present three concrete applications using line darts (1-d darts): relaxed maximal Poisson-disk sampling, high-quality rasterization of depth-of-field blur, and estimation of the probability of failure from a response surface for uncertainty quantification. In these applications, line darts achieve the same fidelity output as point darts in less time. We also demonstrate the accuracy of higher dimensional darts for a volume estimation problem. For Poisson-disk sampling, we use significantly less memory, enabling the generation of larger point clouds in higher dimensions.Comment: 19 pages 16 figure

Optimization techniques for computationally expensive rendering algorithms

Realistic rendering in computer graphics simulates the interactions of light and surfaces. While many accurate models for surface reflection and lighting, including solid surfaces and participating media have been described; most of them rely on intensive computation. Common practices such as adding constraints and assumptions can increase performance. However, they may compromise the quality of the resulting images or the variety of phenomena that can be accurately represented. In this thesis, we will focus on rendering methods that require high amounts of computational resources. Our intention is to consider several conceptually different approaches capable of reducing these requirements with only limited implications in the quality of the results. The first part of this work will study rendering of time-­¿varying participating media. Examples of this type of matter are smoke, optically thick gases and any material that, unlike the vacuum, scatters and absorbs the light that travels through it. We will focus on a subset of algorithms that approximate realistic illumination using images of real world scenes. Starting from the traditional ray marching algorithm, we will suggest and implement different optimizations that will allow performing the computation at interactive frame rates. This thesis will also analyze two different aspects of the generation of anti-­¿aliased images. One targeted to the rendering of screen-­¿space anti-­¿aliased images and the reduction of the artifacts generated in rasterized lines and edges. We expect to describe an implementation that, working as a post process, it is efficient enough to be added to existing rendering pipelines with reduced performance impact. A third method will take advantage of the limitations of the human visual system (HVS) to reduce the resources required to render temporally antialiased images. While film and digital cameras naturally produce motion blur, rendering pipelines need to explicitly simulate it. This process is known to be one of the most important burdens for every rendering pipeline. Motivated by this, we plan to run a series of psychophysical experiments targeted at identifying groups of motion-­¿blurred images that are perceptually equivalent. A possible outcome is the proposal of criteria that may lead to reductions of the rendering budgets

Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm