Hybrid regularization restoration for adaptive optics image

Abstract

The performance of high-resolution imaging with large optical instruments is severely limited by atmospheric turbulence. Adaptive optics (AO) offers a real-time compensation for turbulence. However, the correction is often only partial, and image restoration is required for reaching or nearing to the diffraction limit. In this paper, we consider a hybrid Curvelet-Fourier regularized deconvolution (HCFRD) scheme for use in image restoration problems. The HCFRD algorithm performs noise regularization via scalar shrinkage in both the Fourier and Curvelet domains. The Fourier shrinkage exploits the Fourier transform's economical representation of the colored noise inherent in deconvolution, whereas the curvelet shrinkage exploits the curvelet domain's economical representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and Curvelet regularization by optimizing an approximate mean-squared error (MSE) metric and find that signals with more economical curvelet representations require less Fourier shrinkage. HCFRD is applicable to all ill-conditioned deconvolution problems, its estimate features minimal ringing, unlike the purely Fourier-based Wiener deconvolution. Experimental results prove that HCFRD outperforms the Wiener filter and ForWaRD algorithm in terms of both visual quality and SNR performance.