Visible reconstruction by a circular holographic display from digital holograms recorded under infrared illumination.

A circular holographic display that consists of phase-only spatial light modulators is used to reconstruct images in visible light from digital holograms recorded under infrared (10.6 µm) illumination. The reconstruction yields a holographic digital video display of a three-dimensional ghostlike image of an object floating in space where observers can move and rotate around it.

Perspective projections in the space-frequency plane and fractional Fourier transforms.

Perspective projections in the space-frequency plane are analyzed, and it is shown that under certain conditions they can be approximately modeled in terms of the fractional Fourier transform. The region of validity of the approximation is examined. Numerical examples are presented.

Sampling of the diffraction field.

When optical signals, like diffraction patterns, are processed by digital means the choice of sampling density and geometry is important during analog-to-digital conversion. Continuous band-limited signals can be sampled and recovered from their samples in accord with the Nyquist sampling criteria. The specific form of the convolution kernel that describes the Fresnel diffraction allows another, alternative, full-reconstruction procedure of an object from the samples of its diffraction pattern when the object is space limited. This alternative procedure is applicable and yields full reconstruction even when the diffraction pattern is undersampled and the Nyquist criteria are severely violated. Application of the new procedure to practical diffraction-related phenomena, like in-line holography, improves the processing efficiency without creating any associated artifacts on the reconstructed-object pattern.

Estimation of depth fields suitable for video compression based on 3-D structure and motion of objects.

Intensity prediction along motion trajectories removes temporal redundancy considerably in video compression algorithms. In three-dimensional (3-D) object-based video coding, both 3-D motion and depth values are required for temporal prediction. The required 3-D motion parameters for each object are found by the correspondence-based E-matrix method. The estimation of the correspondences-two-dimensional (2-D) motion field-between the frames and segmentation of the scene into objects are achieved simultaneously by minimizing a Gibbs energy. The depth field is estimated by jointly minimizing a defined distortion and bit-rate criterion using the 3-D motion parameters. The resulting depth field is efficient in the rate-distortion sense. Bit-rate values corresponding to the lossless encoding of the resultant depth fields are obtained using predictive coding; prediction errors are encoded by a Lempel-Ziv algorithm. The results are satisfactory for real-life video scenes.

An improvement to MBASIC algorithm for 3-D motion and depth estimation.

In model-based coding of facial images, the accuracy of motion and depth parameter estimates strongly affects the coding efficiency. MBASIC (model-based analysis-synthesis image coding) is a simple and effective iterative algorithm recently proposed by Aizawa et el. (see Signal Processing: Image Communication, no.1, p.139-52, 1989) for 3-D motion and depth estimation when the initial depth estimates are relatively accurate. In this correspondence, we analyze its performance in the presence of errors in the initial depth estimates and propose a modification to MBASIC algorithm that significantly improves its robustness to random errors with only a small increase in the computational load.

Diffraction from a wavelet point of view: reply to comment.

The two-dimensional field on a plane definitely determines the three-dimensional volume diffraction field, and this fact is clear from the formulation given in my Letter [Opt. Lett. 18, 846 (1993)]. It is also stressed that it is the redundancy of the volume diffraction pattern. The mathematical wavelet domain filtering operation is valid. The optical volume masking is also feasible. However, this does not mean that the wavelet filter function and the three-dimensional optical mask are the same functions.

A respiratory motion artifact reduction method in magnetic resonance imaging of the chest.

An image reconstruction algorithm based on the assumption that the respiratory motion of the chest is linear in space and arbitrary in time is presented. The linear respiratory motion causes phase distortion on the magnetic resonance (MR) data. As a result of this motion, the MR data are the samples of the Fourier transform of the spin density on a nonrectangular grid. In image reconstruction. before taking the inverse Fourier transform, the phase distortion is compensated for, and the rectangular samples are interpolated from the existing nonrectangular samples. A significant amount of motion artifact suppression is achieved with a rough knowledge on the motion using this method. It is demonstrated that the respiratory motion model parameters can be estimated using the information hidden in the motion artifacts.