Point Spread Function Filtering for Radially Variant Blur Restoration

Yupeng Zhang ,Lev Zimin ,Jing Ji ,Satoshi Ikezawa ,T Ueda

doi:10.18494/sam.2013.856

Abstract

In this paper, we present a point spread function (PSF) filtering technique for solving the radially variant blur restoration problem. Radially variant blur is generated by a spherical single-element lens imaging system (SSLIS) that is embedded in an experimental camera module. The restoration of this category of blur is carried out in a polar coordinate system using polar PSFs at different fields of view (FOVs). However, restoration using large PSFs tends to introduce severe ringing artifacts in the restored image owing to the nonsparse nature of these PSFs. We show in this paper that the PSF filtering technique can effectively minimize ringing artifacts by filtering out some PSF pixels with an intensity lower than the threshold intensity. As a result, a nonsparse PSF becomes a sparse PSF, which is for good restoration results. The effectiveness of the PSF filtering technique was validated by visual comparison using three test images captured by the SSLIS camera module. In addition, a systematic way to determine the optimal filtering coefficient for a PSF at any FOV within the FOV range is also introduced.

Highlights

The point spread function (PSF) plays a very important role in the formation and restoration of an image
If the PSF is spatially invariant, the matrix of the PSF takes the form of a block Toeplitz matrix with Toeplitz blocks (BTTB).(7–11) It has been proved in our previous paper that a sparse PSF BTTB results in good restored image quality.[12]. The sparsity of a BTTB can be defined by the ratio of the bandwidth of the BTTB to the number of Toeplitz blocks in the BTTB, denoted β/n
We introduced a PSF filtering technique for restoring a radially expanding blur generated by a spherical single-element lens imaging system (SSLIS)

Summary

Introduction

The point spread function (PSF) plays a very important role in the formation and restoration of an image. In an image formation model, the final recorded scene on the image sensor is a function of the PSF.[1,2,3,4,5,6] The final image quality greatly depends on the size, shape, and intensity of PSFs distributed across the image area. Restoration using a nonsparse BTTB directly introduces strong boundary ringing artifacts across the restored image. Researchers in the field of image restoration have proposed iterative algorithms for reducing the ringing artifacts and gradually improve a restored image until it is similar to the original scene without changing the BTTB sparsity. Reeves proposed an iterative method to gradually approach the true solution of the padded elements of a lexicographically ordered column vector of the degraded image[13] (referred to as “the captured image” in our paper) such that the ringing artifacts are markedly minimized. The iterative method is very effective and efficient for image restoration using a sparse PSF, it is time-consuming when the PSF matrix is not sparse

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Discussion

Conclusion