Restoration of atmospheric turbulence-distorted images via RPCA and quasiconformal maps

Abstract

We address the problem of restoring a high-quality image from an observed image sequence strongly distorted by atmospheric turbulence. A novel algorithm is proposed in this paper to reduce geometric distortion as well as space-and-time-varying blur due to strong turbulence. By considering a suitable energy functional, our algorithm first obtains a sharp reference image and a subsampled image sequence containing sharp and mildly distorted image frames with respect to the reference image. The subsampled image sequence is then stabilized by applying the Robust Principal Component Analysis (RPCA) on the deformation fields between image frames and warping the image frames by a quasiconformal map associated with the low-rank part of the deformation matrix. After image frames are registered to the reference image, the low-rank part of them are deblurred via a blind deconvolution, and the deblurred frames are then fused with the enhanced sparse part. Experiments have been carried out on both synthetic and real turbulence-distorted video. Results demonstrate that our method is effective in alleviating distortions and blur, restoring image details and enhancing visual quality.

On the Applications of Robust PCA in Image and Video Processing

“…• Low-level imaging and analysis: image restoration and denoising [105], [149], [261], [280], [281], texture image denoising [166], hyperspectral image denoising [50], [100], [285], image completion and inpainting [39], [299], image composition for high-dynamic range imaging [21], image decomposition for intrinsic image computation [151], [313] and for structural image decomposition [43], image alignment and rectification [219], [231], [259], [293], [328], image stitching and mosaicking [163], image colorization [306], multi-focus image [277], [278], [325], [326], [327], pansharpening [322], change detection [51], face recognition [185], [289], [320], partial-duplicate image search [302], image saliency detection [147], [160], [161], [222], [228] and image analysis [343], [173]. • Medical imaging: RPCA has become a powerful tool to increase the performance of data acquisition [89], [90], [210],…”

“…There are two main kinds of degradations: geometric distortion and blur. Lau et al [149] addressed the degradation issues by first optimizing a mathematical model to subsample sharp and mildly distorted video frames, and then applying a two-step stabilization to stabilize the subsampled video with Beltrami coefficients, replacing blurry images with sharp ones by optical flow and robust PCA. In particular, for every frame I samp k , Lau et al [149] calculated the deformation fields V j k from a fixed frame I samp k to other ones.…”

“…Lau et al [149] addressed the degradation issues by first optimizing a mathematical model to subsample sharp and mildly distorted video frames, and then applying a two-step stabilization to stabilize the subsampled video with Beltrami coefficients, replacing blurry images with sharp ones by optical flow and robust PCA. In particular, for every frame I samp k , Lau et al [149] calculated the deformation fields V j k from a fixed frame I samp k to other ones. Define distorted and blurred image, Sobolev gradient-Laplacian method [184], Centroid method [195] deblurred [248], Two-stage reconstruction method [206] and RPCA algorithm [149] (Images from Lau et al [149]).…”

“…In particular, for every frame I samp k , Lau et al [149] calculated the deformation fields V j k from a fixed frame I samp k to other ones. Define distorted and blurred image, Sobolev gradient-Laplacian method [184], Centroid method [195] deblurred [248], Two-stage reconstruction method [206] and RPCA algorithm [149] (Images from Lau et al [149]).…”

“…is the nuclear norm, i.e, sum of singular values, S 1 = ij |S i,j | is the 1 -norm, and the sparse part S * k,p corresponds to the outlier. Lau et al [149] then warped I samp k by a post-processing of low-rank part L k for each k to obtain the stabilized frames. Experiments on both synthetic and real experiments demonstrate the effectiveness of the proposed method in alleviating distortions and blur, restoring image details and enhancing visual quality against several state-of-art methods as can be seen in Fig 1. Image denoising is a problem closely related to image restoration, where the degradation is caused by noise.…”