Reconstruction Constraints Research Articles

Design of short tap perfect reconstruction filters for subband coding of images

AbstractShort tap filters reduce the computational complexity of filtering processes and also reduce image degradations associated with ringing effects near edges in image subband coding. When the number of taps is reduced, however, coding performance generally deteriorates. In this paper, short tap filters that satisfy isolated perfect reconstruction constraints are designed so as to improve coding performance. For the sake of comparisons, linear phase‐ and orthogonal filters are also designed. Filters with coefficients determined by the values 2 n are designed to reduce further the computational burden of the filter process. Assuming that the input can be modeled by an AR(1) process, the set of parameters which determine the tap coefficients are selected to maximize the coding gain. the relationship between signal‐to‐noise ratio and entropy is determined to evaluate coding performance. the superior coding performance of the perfect reconstruction filters shows no degradation when subjected to an integer coefficient constraint. Also, filters with coefficients determined by the values 2 n and excellent coding performance are obtained.

Short-time Fourier transform and wavelet transform with Fourier-domain processing

We discuss the semicontinuous short-time Fourier transform (STFT) and the semicontinual wavelet transform (WT) with Fourier-domain processing, which is suitable for optical implementation. We also systematically analyze the selection of the window functions, especially those based on the biorthogonality and the orthogonality constraints for perfect signal reconstruction. We show that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal window function in the time domain. The merit of a biorthogonal window is that it could simplify the inverse STFT and the inverse WT. A couple of optical architectures based on Fourier-domain processing for the STFT and the WT, by which real-time signal processing can be realized, are proposed.

A system model and inversion for synthetic aperture radar imaging

A system model and its corresponding inversion for synthetic aperture radar (SAR) imaging are presented. The system model incorporates the spherical nature of a radar's radiation pattern at far field. The inverse method based on this model performs a spatial Fourier transform (Doppler processing) on the recorded signals with respect to the available coordinates of a translational radar (SAR) or target (inverse SAR). It is shown that the transformed data provide samples of the spatial Fourier transform of the target's reflectivity function. The inverse method can be modified to incorporate deviations of the radar's motion from its prescribed straight line path. The effects of finite aperture on resolution, reconstruction, and sampling constraints for the imaging problem are discussed.

Lagrange multiplier approaches to the design of two-channel perfect-reconstruction linear-phase FIR filter banks

The authors present two approaches to the design of two-channel perfect-reconstruction linear-phase finite-impulse-response (FIR) filter banks. Both approaches analyze and design the impulse responses of the analysis filter bank directly. The synthesis filter bank is then obtained by simply changing the signs of odd-order coefficients in the analysis filter bank. The approach deals with unequal-length filter banks. By designing the lower length filters first, one can take advantage of the fact that the number of variables for designing the higher length filters is more than the number of perfect-reconstruction constraint equations. The second approach generalizes the first, and covers the design for all parts of linear phase perfect reconstruction constraint equations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bistatic synthetic aperture radar inversion with application in dynamic object imaging

An inversion method is presented for bistatic synthetic aperture radar imaging. The method is based on a Fourier analysis (Doppler processing) of the bistatic synthesized array's data followed by a phase modulation analysis of the Doppler data. The approach incorporates the phase information of the wavefront curvature in the transmitted waves as well as the resultant echoed signals. The Doppler data are shown to provide samples of the reflectivity function's spatial Fourier transform within a band that depends upon the bistatic angles and ranges. Associated resolution, reconstruction, and sampling constraints for the imaging problem are discussed. The bistatic SAR inversion is also utilized to formulate an inversion for multistatic measurements made along a physical linear array due to a single transmission to image a dynamic object. >

Reconstruction and sampling constraints for spiral data (image processing)

The author addresses the problem of reconstructing a circularly bandlimited two-dimensional function from its samples on a general spiral contour. The spiral data are represented in terms of evenly spaced samples from a nonlinear two-dimensional transformation of the Cartesian coordinates. This transformation makes it possible to use unified Fourier reconstruction sampling principles to obtain accurate reconstruction based on a set of constraints imposed on the spiral parameters. The results are then utilized to develop efficient sampling strategies for the linear class of spirals, the spiral of Archimedes. Sampling efficiency for spiral data, analogous to the sampling efficiencies of hexagonally and rectangularly sampled data, is defined. A sampling scheme on a spiral is introduced that possesses a uniform sampling efficiency comparable to the sampling efficiency of rectangularly sampled data. >

Density profile reconstructions from 2-D interferometric data on Microtor using novel tomographic analysis techniques

Plasma tomographic reconstructions are subject to aliasing ambiguity as a result of the limited angular and radial sampling rates for the line-integrated data. The two-view interferometer installed on the Microtor tokamak yields unambiguous information, specifically, a collection of six low-order alias-free moments of the 2-D electron density distribution. The unspoiled coefficients can be related to physically intuitive quantities and so yield information pertinent to the equilibrium and dynamical behavior of the plasma column. Alternatively, they can be used as constraints for a maximum entropy reconstruction of the source to produce an image free of aliasing artifacts.

Density profile reconstructions from 2-D interferometric data on Microtor using novel tomographic analysis techniques (abstract)

Plasma tomographic reconstructions are subject to aliasing ambiguity as a result of the limited angular and radial sampling rates for the line-integrated data. The two-view interferometer installed on the Microtor tokamak yields unambiguous information, specifically, a collection of six low-order alias-free moments of the 2-D electron density distribution. The unspoiled coefficients can be related to physically intuitive quantities and so yield information pertinent to the equilibrium and dynamical behavior of the plasma column. Alternatively, they can be used as constraints for a maximum entropy reconstruction of the source to produce an image free of aliasing artifacts.

Testing for support irreducibility

An irreducible support is one that ensures a unique solution to the phase problem without requiring that it be explicitly imposed as a reconstruction constraint. However, the only nontrivial support that has been shown to be irreducible is Eisenstein’s support. Herein a general description of support irreducibility is developed for discrete functions, both over positive, real and over complex numbers. In addition, a method of testing an arbitrary support of finite extent for irreducibility is introduced, and a number of simple irreducible supports are presented that are not of the Eisenstein type.

The use of non-local constraints in maximum-entropy electron density reconstruction

Different expressions of the maximum-entropy estimates of the electron density function, corresponding to different prior information are obtained. They show that no general-purpose configurational entropy of density maps exists. Some universal properties of the modellings are discussed. In particular, the meaning of super-resolution is clarified. The information of lower and upper bounds of the electron density is not in general strong enough to produce atomic maps. Atomicity is then introduced as non-local constraints and applied to the problem of phase extension using experimental data and low-resolution model phases. In all cases, the knowledge of phases up to 3.5-3 Å and observed moduli up to 1.5-1 Å allows an estimate of the electron density of roughly the same quality as the 1 Å map obtained from a Fourier summation to be produced.

Cretaceous sedimentation and tectonics, Tyaughton–Methow Basin, southwestern British Columbia

The Mesozoic Tyaughton–Methow Basin straddles the Fraser–Yalakom–Pasayten – Straight Creek (FYPSC) strike-slip fault zone between six tectono-stratigraphic terranes in southwestern British Columbia. Data from Hauterivian–Cenomanian basin fill provide constraints for reconstruction of fault displacement and paleogeography.The Early Cretaceous eastern margin of the basin was a region of uplifted Jurassic plutons and active intermediate volcanism. Detritus shed southwestward from that margin was deposited as the marine Jackass Mountain Group. Albian inner to mid-fan facies of the Jackass Mountain Group can be correlated across the Yalakom Fault, suggesting 150 ± 25 km of post- Albian dextral offset. Deposits of the Jackass Mountain Group overlap the major strike- slip zone (FYPSC). If that zone represents the eastern boundary of the tectono-stratigraphic terrane, Wrangellia, then accretion of Wrangellia to terranes to the east occurred before late Early Cretaceous time.The western margin of the basin first became prominent with Cenomanian uplift of the Coast Mountain suprastructure. Uplift is recorded by dispersal patterns of the volcaniclastic Kingsvale Group southwest of the Yalakom Fault.Reversing 110 km of Late Cretaceous – early Tertiary dextral motion on the Fraser – Straight Creek Fault followed by 150 km of Cenomanian – Turonian motion on the Yalakom – Ross Lake Fault restores the basin to a reasonable depositional configuration.

Kinematics of plate convergence deduced from Mesozoic structures in the Western Cordillera

Mesozoic structures in the western Cordillera of the United States yield important constraints for kinematic reconstruction of plate motions relative to North America. Structures in the Mesozoic arc(s) of the northern Sierra Nevada and of northeastern Oregon are remarkably uniform in timing, style, and with Late Cretaceous and/or Cenozoic rotations removed, orientation. Rocks of both regions experienced three major episodes of contraction occurring in the Triassic‐Early Jurassic, the Late Jurassic, and the Early Cretaceous. Cross folds were developed after the first two deformations but were not associated with significant shortening. The three major deformations are nearly homoaxial and have shortening axes oriented subperpendicular (NE‐SW) to the regional trend of the arc system. In the back arc region of the northwestern Great Basin, deposition was continuous during the Triassic and Early Jurassic, and the region was shielded from tectonism in the arc to the west. Development of a regional fold‐thrust belt associated with major NW‐SE shortening was initiated in the back arc region during the Middle or Late Jurassic and continued through the Early Cretaceous. Corresponding deformation did not occur in the arc, and the arc and back arc were decoupled by a major left‐lateral fault system that subparallelled the arc axis. In the mid‐Cretaceous (approximately 100 m.y. B.P.), regional compression in the back arc abruptly changed to NE‐SW, and both the arc and back arc experienced major shortening. Development of homoaxial structures in the Sierran arc is probably analogous to shortening in present‐day arc systems undergoing oblique subduction, in which the shortening axis is parallel to the normal component of convergence. Thus the dominant structures in the Sierran arc simply may be a reflection of the orientation of the trench and may not constrain the sense of obliquity of convergence. Strike‐slip faults and related compressional structures, such as the back arc left‐lateral fault and associated fold‐thrust belt, are probably the response to the strike‐slip component of convergence and indicate a period of left‐oblique subduction. Relative plate motions constrained by paleomagnetic data are in agreement with regional structures and indicate strong right‐lateral components of motion for the last 100 m.y. Before 100 m.y. B.P., relative plate motions are inadequately constrained by paleomagnetic data and regional structures indicate a period of left‐oblique convergence from the Middle or Late Jurassic to approximately 100 m.y. B.P. During the Triassic and Early Jurassic the relative sense of convergence is equivocal and the possibility exists that continuous left‐oblique convergence occurred throughout the late Paleozoic and early Mesozoic (until 100 m.y. B.P.). Based on the available data, we cannot discount the possibility that a complex convergence history existed, however, with changes from right to left convergence in the Middle or Late Jurassic and from left to right convergence in the mid‐Cretaceous.

The Use of Multispectral Imaging in Limited-Angle Reconstruction

It is known that some Fourier components of an object are missing from its projection data in CT imaging if the object can be scanned only in a restricted angular range. Due to the ill-conditioning of the problem, the accuracy of extrapolating the missing Fourier components from the known ones is limited by the precision of both the measured data and the computing device used. In this paper we propose a method for improving limited-angle reconstruction by separating out individual component substances in the object through multiple energy scans. It is shown that reconstructing individual component substances can be done more accurately than reconstructing the composite object. The use of nonlinear constraints in reconstruction is discussed. The method can be applied to modalities such as x-ray scanning, electron microscopy, ultrasound imaging, and neutron imaging.