Levent Onural

Optimal filtering in fractional Fourier domains

For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N/sup 2/) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N log N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained.

Digital Decoding Of In-Line Holograms

Digitally sampled in-line holograms may be linearly filtered to reconstruct a representation of the original object distribution, thereby decoding the information contained in the hologram. The decoding process is performed by digital computation rather than optically. Substitution of digital for optical decoding has several advantages, including selective suppression of the twin-image artifact, elimination of the far-field requirement, and automation of the data reduction and analysis process. The proposed filter is a truncated series expansion of the inverse of that operator that maps object opacity function to hologram intensity. The first term of the expansion is shown to be equivalent to conventional (optical) reconstruction, with successive terms increasingly sup-pressing the twin image. The algorithm is computationally efficient, requiring only a single fast Fourier transform pair.

Image sequence analysis for emerging interactive multimedia services-the European COST 211 framework

Flexibility and efficiency of coding, content extraction, and content-based search are key research topics in the field of interactive multimedia. Ongoing ISO MPEG-4 and MPEG-7 activities are targeting standardization to facilitate such services. European COST Telecommunications activities provide a framework for research collaboration. At present a significant effort of the COST 211/sup ter/ group activities is dedicated toward image and video sequence analysis and segmentation-an important technological aspect for the success of emerging object-based MPEG-4 and MPEG-7 multimedia applications. The current work of COST 211 is centered around the test model, called the analysis model (AM). The essential feature of the AM is its ability to fuse information from different sources to achieve a high-quality object segmentation. The current information sources are the intermediate results from frame-based (still) color segmentation, motion vector based segmentation, and change-detection-based segmentation. Motion vectors, which form the basis for the motion vector based intermediate segmentation, are estimated from consecutive frames. A recursive shortest spanning tree (RSST) algorithm is used to obtain intermediate color and motion vector based segmentation results. A rule-based region processor fuses the intermediate results; a postprocessor further refines the final segmentation output. The results of the current AM are satisfactory.

State of the Art in Holographic Displays: A Survey

True-3D imaging and display systems are based on physical duplication of light distribution. Holography is a true-3D technique. There are significant developments in electro-holographic displays in recent years. Liquid crystal, liquid crystal on silicon, optically addressed, mirror-based, holographic polymer-dispersed, and acousto-optic devices are used as holographic displays. There are complete electro-holographic display systems and some of them are already commercialized.

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.

Real-time phase-only color holographic video display system using LED illumination

A real-time full-color phase-only holographic display system generates holograms of 3D objects. The system includes a 3D object formed by voxels, an internet-based transmission capability that transmits the object information to the server, a real-time hologram generation unit, and a holographic display unit with incoherent illumination. The server calculates three phase holograms for RGB components using multiple GPUs. The resultant phase holograms are saved into an RGB bitmap image and loaded to the phase-only spatial light modulators (SLMs). SLMs are illuminated uniformly by LEDs, and reconstructed waves are aligned and overlapped by using high precision optics and stages. Experimental results are satisfactory.

Circular holographic video display system

A circular holographic video display system reconstructs holographic video. Phase-only spatial light modulators are tiled in a circular configuration in order to increase the field of view. A beam-splitter is used to align the active area of the SLMs side by side without any gap. With the help of this configuration observers can see 3D ghost-like image floating in space and can move and rotate around the object. The 3D reconstructions can be observed binocularly. Experimental results are satisfactory.

Design and implementation of a general-purpose median filter unit in CMOS VLSI

A general-purpose median filter unit configuration in the form of two single-chip median filters, one extensible and one real time, is described. The networks of the chips are pipelined and systolic at bit level and based on odd/even transposition sorting. The chips are implemented in 3- mu m standard CMOS using full-custom VLSI design techniques. The exact median of elements, in a window size w=9 with arbitrary word length L, can be found using only one extensible median filter chip. The filter can be extended to arbitrary window size and word lengths by using many chips. Simulation results show that the extensible median filter chip can be clocked up to 40 MHz and can generate 30/L megamedians per second. The real-time median filter chip can find the exact running medians of elements in a window of a fixed size w=9 with L=8. Simulations show that it can generate up to 50 megamedians per second with a 50-MHz clock. The algorithms, VLSI implementations, and chip test results are presented, along with some possible applications. >

Diffraction from a wavelet point of view

The system impulse response representing the Fresnel diffraction is shown to form a wavelet family of functions. The scale parameter of the wavelet family represents the depth (distance). This observation relates the diffraction-holography-related studies and the wavelet theory. The results may be used in various optical applications such as designing robust volume optical elements for optical signal processing and finding new formulations for optical inverse problems. The results also extend the wavelet concept to the nonbandpass family of functions with the implication of new applications in signal processing. The presented wavelet structure, for example, is a tool for space–depth analysis.

Digital Holographic Three-Dimensional Video Displays

Holography aims to record and regenerate volume filling light fields to reproduce ghost-like 3-D images that are optically indistinguishable from their physical 3-D originals. Digital holographic video displays are pixelated devices on which digital holograms can be written at video rates. Spatial light modulators (SLMs) are used for such purposes in practice; even though it is desirable to have SLMs that can modulate both the phase and amplitude of the incident light at each pixel, usually amplitude-only or phase-only SLMs are available. Many laboratories have reported working prototypes using different designs. Size and resolution of the SLMs are quite demanding for satisfactory 3-D reconstructions. Space-bandwidth product (SBP) seems like a good metric for quality analysis. Even though moderate SBP is satisfactory for a stationary observer with no lateral or rotational motion, the required SBP quickly increases when such motion is allowed. Multi-SLM designs, especially over curved surfaces, relieve high bandwidth requirements, and therefore, are strong candidates for futuristic holographic video displays. Holograms are quite robust to noise and quantization. It is demonstrated that either laser or light-emitting diode (LED) illumination is feasible. Current research momentum is increasing with many exciting and encouraging results.