Iftach Klapp

Design of an image restoration algorithm for the TOMBO imaging system

The TOMBO system (thin observation module by bound optics) is a multichannel subimaging system over a single electronic imaging device. Each subsystem provides a low-resolution (LR) image from a unique lateral point of view. By estimating the images lateral position, a high-resolution (HR) image is restored from the series of the LR images. This paper proposes an multistage algorithm comprised of successive stages, improving difficulties in previous suggested schemes. First, the registration algorithm estimates the subchannel shift parameters and eliminates bias. Second, we introduce a fast image fusion, overcoming visual blockiness artifacts that characterized previously suggested schemes. The algorithm fuses the set of sampled subchannel images into a single image, providing the reconstruction initial estimate. Third, an edge-sensitive quadratic upper bound term to the total variation regulator is suggested. The complete algorithm allows the reconstruction of a clean, HR image, in linear computation time, by the use of the linear conjugate gradient optimization. Finally, we present a simulated comparison between the proposed method and a previously suggested image restoration method. The results show that the proposed method yields better reconstruction fidelity while eliminating spatial speckle artifacts associated with the previously suggested method.

Deblurring space-variant blur by adding noisy image

Imaging restoration is an essential step in hybrid optical and image processing system which relays on poor optics. The poor optics makes the blur ill-conditioned and turns the deblurring process difficult and unstable. Recently the idea of parallel optics (PO) was introduced. In the parallel optics setup the optical system is composed of a main system and an auxiliary system. The auxiliary system is designed to improve the stability of the deblurring process by improving the condition number of the blurring operator. In this paper we show that in one such system the post processing acts as a noise filter hence allows to work with noisy data in the auxiliary channel. Using the singular value decomposition we derive analytical limit for the difference in SNR requirements of the auxiliary channel relative to that of the main channel. The gap between the SNR requirements of the two systems is analyzed theoretically and proved to be as large as 27.68 [db]. Image restoration comparison on simulations is performed between a blurred/noisy pair with average SNR gap of 20 [db] and a system without an auxiliary system. The average Mean Square Error Improvement Factor (MSEIF) achieved by the blurred/noisy pair, was 13.9 [db] higher than the system without a noisy auxiliary system.

Trajectories in parallel optics

In our previous work we showed the ability to improve the optical systems matrix condition by optical design, thereby improving its robustness to noise. It was shown that by using singular value decomposition, a target point-spread function (PSF) matrix can be defined for an auxiliary optical system, which works parallel to the original system to achieve such an improvement. In this paper, after briefly introducing the all optics implementation of the auxiliary system, we show a method to decompose the target PSF matrix. This is done through a series of shifted responses of auxiliary optics (named trajectories), where a complicated hardware filter is replaced by postprocessing. This process manipulates the pixel confined PSF response of simple auxiliary optics, which in turn creates an auxiliary system with the required PSF matrix. This method is simulated on two space variant systems and reduces their system condition number from 18,598 to 197 and from 87,640 to 5.75, respectively. We perform a study of the latter result and show significant improvement in image restoration performance, in comparison to a system without auxiliary optics and to other previously suggested hybrid solutions. Image restoration results show that in a range of low signal-to-noise ratio values, the trajectories method gives a significant advantage over alternative approaches. A third space invariant study case is explored only briefly, and we present a significant improvement in the matrix condition number from 1.9160e+013 to 34,526.

Trajectories by a blurred auxiliary system

Simple optical imaging systems tend to suffer from a space variant (SV) blur and ill matrix condition and, thus, tend to amplify additive noise in the essential stage of image restoration. Previously, we showed that the matrix condition of systems with SV blur can be improved by adding a system-tailored parallel auxiliary system. We introduced such a solution with the “trajectories” method, where we used auxiliary optics with a pixel confined point spread function to decompose the required auxiliary system. In this paper, by removing the pixel confined requirement, we extend the trajectories to a “blurred trajectories” method, which relies on the more common case of auxiliary optics with blurred response. The method is simulated and shown to be effective in two cases. First, we show that the matrix condition is significantly improved. In one case the condition number of a space variant system is reduced from 87640 down to 1212. In a second case of a highly defocused system, the matrix condition number is reduced from 6412.5 to 238.7. We then investigate the influence of the improvement in the matrix condition on image restoration by regularization with and without the auxiliary system. Blurred trajectories with regularization yields better restoration than regularization only. The new (to our knowledge) system is compared to other previously suggested optical designs. The method’s flexibility is demonstrated when applied as postprocessing on a system that includes the original ill-conditioned system and a quartic phase filter and yields an improvement in the overall matrix condition.