A General Theory Of Time-sequential Sampling
ABSTRACT In this paper, we consider the problem of optimum sampling of spatio-temporal signals. Recently, there has been increasing interest in this topic due to the advent of next generation television systems. Time-sequential sampling is a sampling paradigm in which samples are taken from the signal, one at a time, according to a prescribed ordering which is repeated after one complete frame of data is acquired. This paper extends previous work on time-sequential sampling to include arbitrary periodic patterns, as well as sampling on lattices with arbitrary geometries. As a result, a unifying theory is developed which includes such classical field-instantaneous lattices as field-quincunx and line-quincunx, proposed for downsampling of high-definition television signals, as specific examples. Such a formulation provides a systematic way for studying the aliasing effects of the ordering in which a signal is sampled. The design and analysis of these patterns is facilitated by introducing a powerful technique from the geometry of numbers which permits these tasks to be carried out in a coordinate system where the time-sequential patterns are rectangularly periodic. The resulting anti-aliasing patterns have a congruential structure. By further extending the theory to include time-sequential sampling on selected cosets of a lattice, we can analyze sampling patterns which are not true lattices, such as the bit-reversed sampling pattern.
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- "In this paper, we address DCT coding of images sampled on arbitrary lattices. To this effect, we discuss an efficient method for the computation of the DCT on nonrectangular sampling grids, which is similar to the computation of the M- D DFI' in nonrectangular grids , . The method is based on the Smith-normal decomposition, that is, diagonalizing the periodicity matrix of the M-D sequence. "
ABSTRACT: Discrete cosine transform (DCT) coding is widely used for compression of rectangularly sampled images. We address efficient DCT coding of nonrectangularly sampled images. To this effect, we discuss an efficient method for the computation of the DCT on nonrectangular sampling grids using the Smith-normal decomposition. Simulation results are provided.< >IEEE Signal Processing Letters 10/1994; 1(9-1):131 - 133. DOI:10.1109/97.319026 · 1.64 Impact Factor
Conference Paper: Dynamic imaging by object modeling and estimation.[Show abstract] [Hide abstract]
ABSTRACT: This paper presents a novel dynamic imaging method. This method models the object by a time-varying function, thus converting the dynamic imaging problem to a parameter identification problem. Experimental results demonstrate that this method can produce time-sequential images from a time-varying object with both high temporal and spatial resolution. The proposed method has been validated in magnetic resonance imaging by computer simulation, phantom study and animal studyImage Processing, 1995. Proceedings., International Conference on; 01/1995
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ABSTRACT: Determining the parameters of motion within a time-varying scene is an important problem in such fields as computer vision, motion compensated video coding, and tracking. Most motion estimation algorithms operate on image data that has been sampled in both space and time. However, very little work has been done to investigate the impact of the underlying sampling strategy on the motion estimation problem. The authors investigate motion estimation with time-sequentially sampled image data. They consider both centroid-displacement-based and Fourier-based approaches to motion estimation with this type of data. For comparision, they also examine the performance of these estimators with conventional, frame-instantaneously sampled data. The motion estimators are developed and evaluated in the context of the tracking problem. In particular, they present extensive numerical results showing the performance of the motion estimators in a simulated tracking environment within which the assumptions underlying the development of the estimators are violated. These results suggest empirical rules for choosing parameter values for the estimators.IEEE Transactions on Image Processing 02/1995; 4(1):48-65. DOI:10.1109/83.350814 · 3.11 Impact Factor