Todd C. Torgersen

Iterative image restoration using approximate inverse preconditioning

Removing a linear shift-invariant blur from a signal or image can be accomplished by inverse or Wiener filtering, or by an iterative least-squares deblurring procedure. Because of the ill-posed characteristics of the deconvolution problem, in the presence of noise, filtering methods often yield poor results. On the other hand, iterative methods often suffer from slow convergence at high spatial frequencies. This paper concerns solving deconvolution problems for atmospherically blurred images by the preconditioned conjugate gradient algorithm, where a new approximate inverse preconditioner is used to increase the rate of convergence. Theoretical results are established to show that fast convergence can be expected, and test results are reported for a ground-based astronomical imaging problem.

Engineering the pupil phase to improve image quality

By suitably phase-encoding optical images in the pupil plane and then digitally restoring them, one can greatly improve their quality. The use of a cubic phase mask originated by Dowski and Cathey to enhance the depth of focus in the images of 3-d scenes is a classic example of this powerful approach. By using the Strehl ratio as a measure of image quality, we propose tailoring the pupil phase profile by minimizing the sensitivity of the quality of the phase-encoded image of a point source to both its lateral and longitudinal coordinates. Our approach ensures that the encoded image will be formed under a nearly shift-invariant imaging condition, which can then be digitally restored to a high overall quality nearly free from the aberrations and limited depth of focus of a traditional imaging system. We also introduce an alternative measure of sensitivity that is based on the concept of Fisher information. In order to demonstrate the validity of our general approach, we present results of computer simulations that include the limitations imposed by detector noise.

Computational imaging systems for iris recognition

Computational imaging systems are modern systems that consist of generalized aspheric optics and image processing capability. These systems can be optimized to greatly increase the performance above systems consisting solely of traditional optics. Computational imaging technology can be used to advantage in iris recognition applications. A major difficulty in current iris recognition systems is a very shallow depth-of-field that limits system usability and increases system complexity. We first review some current iris recognition algorithms, and then describe computational imaging approaches to iris recognition using cubic phase wavefront encoding. These new approaches can greatly increase the depth-of-field over that possible with traditional optics, while keeping sufficient recognition accuracy. In these approaches the combination of optics, detectors, and image processing all contribute to the iris recognition accuracy and efficiency. We describe different optimization methods for designing the optics and the image processing algorithms, and provide laboratory and simulation results from applying these systems and results on restoring the intermediate phase encoded images using both direct Wiener filter and iterative conjugate gradient methods.

Pupil-phase optimization for extended-focus, aberration-corrected imaging systems

The insertion of a suitably designed phase plate in the pupil of an imaging system makes it possible to encode the depth dimension of an extended three-dimensional scene by means of an approximately shift-invariant PSF. The so-encoded image can then be deblurred digitally by standard image recovery algorithms to recoup the depth dependent detail of the original scene. A similar strategy can be adopted to compensate for certain monochromatic aberrations of the system. Here we consider two approaches to optimizing the design of the phase plate that are somewhat complementary - one based on Fisher information that attempts to reduce the sensitivity of the phase encoded image to misfocus and the other based on a minimax formulation of the sum of singular values of the system blurring matrix that attempts to maximize the resolution in the final image. Comparisons of these two optimization approaches are discussed. Our preliminary demonstration of the use of such pupil-phase engineering to successfully control system aberrations, particularly spherical aberration, is also presented.

High-Resolution Imaging Using Integrated Optical Systems

Certain optical aberrations, such as defocus, can significantly degrade the signal collected by an imaging system, producing images with low resolution. In images with depth‐dependent detail, such degradations are difficult to remove due to their inherent spatially varying nature. In 1995, Dowski and Cathey introduced the concept of wavefront coding to extend the depth of field. They showed that wavefront coding and decoding enables quality control of such images using integrated optical‐digital imaging systems. With wavefront coding, a high‐resolution image can be efficiently obtained without the need to resort to expensive algorithms for spatially varying restoration. In this article, we discuss a novel and effective multiple‐design‐parameter approach for optimizing the processes of encoding and decoding the wavefront phase in integrated optical‐digital imaging systems. Our approach involves the use of information metrics, such as the Strehl ratio and Fisher information, for determining the optimal pupil‐phase distribution for which the resulting image is insensitive to certain aberrations, such as focus errors. The effectiveness of this approach is illustrated with a number of numerical simulation experiments, and applications to the development of iris recognition systems with high‐resolution capabilities are briefly discussed.

Extended Evaluation of Simulated Wavefront Coding Technology in Iris Recognition

The iris is a popular biometric that has been demonstrated to exhibit high matching accuracy and permanence under appropriate conditions. However, there are several limiting factors that are yet to be comprehensively addressed. One major drawback, in standard limited-focus iris recognition systems, is the restrictions imposed by the optical parameters of the acquisition system on the depth of field. Recently, wavefront coding technology has been proposed as a method to extend the depth of field of such limited-focus imaging systems. In this work we examine the utilization of a simulated wavefront coded element for increasing the operational range of iris recognition, without affecting the computational requirements of the system. A statistically relevant dataset of 150 iris images from 50 subjects is employed in a simulation study to determine the matching performance of a standard limited-focus system and a wavefront coded iris imaging system over an extended depth of field. It is shown that the operational range for iris recognition can be significantly increased, without the need to post-process the wavefront coded imagery.

High-resolution iris image reconstruction from low-resolution imagery

We investigate the use of a novel multi-lens imaging system in the context of biometric identification, and more specifically, for iris recognition. Multi-lenslet cameras offer a number of significant advantages over standard single-lens camera systems, including thin form-factor and wide angle of view. By using appropriate lenslet spacing relative to the detector pixel pitch, the resulting ensemble of images implicitly contains subject information at higher spatial frequencies than those present in a single image. Additionally, a multi-lenslet approach enables the use of observational diversity, including phase, polarization, neutral density, and wavelength diversities. For example, post-processing multiple observations taken with differing neutral density filters yields an image having an extended dynamic range. Our research group has developed several multi-lens camera prototypes for the investigation of such diversities. In this paper, we present techniques for computing a high-resolution reconstructed image from an ensemble of low-resolution images containing sub-pixel level displacements. The quality of a reconstructed image is measured by computing the Hamming distance between the Daugman4 iris code of a conventional reference iris image, and the iris code of a corresponding reconstructed image. We present numerical results concerning the effect of noise and defocus blur in the reconstruction process using simulated data and report preliminary work on the reconstruction of actual iris data obtained with our camera prototypes.

Integrated optical-digital approaches for enhancing image restoration and focus invariance

A novel and successful optical-digital approach for removing certain aberrations in imaging systems involves placing an optical mask between an image-recording device and an object to encode the wavefront phase before the image is recorded, followed by digital image deconvolution to decode the phase. We have observed that when appropriately engineered, such an optical mask can also act as a form of preconditioner for certain deconvolution algorithms. It can boost information in the signal before it is recorded well above the noise level, leveraging digital restorations of very high quality. In this paper, we 1) examine the influence that a phase mask has on the incoming signal and how it subsequently affects the performance of restoration algorithms, and 2) explore the design of optical masks, a difficult nonlinear optimization problem with multiple design parameters, for removing certain aberrations and for maximizing restorability and information in recorded images.

PERIODIC: Integrated Computational Array Imaging Technology

An array imaging system, dubbed PERIODIC, is presented, capable of exploiting diversities, including subpixel displacement, phase, polarization, and wavelength, to produce superresolution images. The hardware system and software interface described, and sample results are shown.

A practical enhanced-resolution integrated optical-digital imaging camera (PERIODIC)

An integrated array computational imaging system, dubbed PERIODIC, is presented which is capable of exploiting a diverse variety of optical information including sub-pixel displacements, phase, polarization, intensity, and wavelength. Several applications of this technology will be presented including digital superresolution, enhanced dynamic range and multi-spectral imaging. Other applications include polarization based dehazing, extended depth of field and 3D imaging. The optical hardware system and software algorithms are described, and sample results are shown.