Yifei Lou

Image Recovery via Nonlocal Operators

This paper considers two nonlocal regularizations for image recovery, which exploit the spatial interactions in images. We get superior results using preprocessed data as input for the weighted functionals. Applications discussed include image deconvolution and tomographic reconstruction. The numerical results show our method outperforms some previous ones.

A note on multi-image denoising

Taking photographs under low light conditions with a hand-held camera is problematic. A long exposure time can cause motion blur due to the camera shaking and a short exposure time gives a noisy image. We consider the new technical possibility offered by cameras that take image bursts. Each image of the burst is sharp but noisy. In this preliminary investigation, we explore a strategy to efficiently denoise multi-images or video. The proposed algorithm is a complex image processing chain involving accurate registration, video equalization, noise estimation and the use of state-of-the-art denoising methods. Yet, we show that this complex chain may become risk free thanks to a key feature: the noise model can be estimated accurately from the image burst. Preliminary tests will be presented. On the technical side, the method can already be used to estimate a non parametric camera noise model from any image burst.

Direct Sparse Deblurring

We propose a deblurring algorithm that explicitly takes into account the sparse characteristics of natural images and does not entail solving a numerically ill-conditioned backward-diffusion. The key observation is that the sparse coefficients that encode a given image with respect to an over-complete basis are the same that encode a blurred version of the image with respect to a modified basis. Following an “analysis-by-synthesis” approach, an explicit generative model is used to compute a sparse representation of the blurred image, and its coefficients are used to combine elements of the original basis to yield a restored image.

A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing

We propose a weighted difference of anisotropic and isotropic total variation (TV) as a regularization for image processing tasks, based on the well-known TV model and natural image statistics. Due to the form of our model, it is natural to compute via a difference of convex algorithm (DCA). We draw its connection to the Bregman iteration for convex problems and prove that the iteration generated from our algorithm converges to a stationary point with the objective function values decreasing monotonically. A stopping strategy based on the stable oscillatory pattern of the iteration error from the ground truth is introduced. In numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction, our method improves on the classical TV model consistently and is on par with representative state-of-the-art methods.

Nonlocal Similarity Image Filtering

We exploit the recurrence of structures at different locations, orientations and scales in an image to perform denoising. While previous methods based on nonlocal filtering identify corresponding patches only up to translations, we consider more general similarity transformations. Due to the additional computational burden, we break the problem down into two steps: First, we extract similarity invariant descriptors at each pixel location; second, we search for similar patches by matching descriptors. The descriptors used are inspired by scale-invariant feature transform (SIFT), whereas the similarity search is solved via the minimization of a cost function adapted from local denoising methods. Our method compares favorably with existing denoising algorithms as tested on several datasets.

Phase Retrieval from Incomplete Magnitude Information via Total Variation Regularization

The phase retrieval problem has drawn considerable attention, as many optical detection devices can only measure magnitudes of the Fourier transform of the underlying object (signal or image). This paper addresses the phase retrieval problem from incomplete data, where only partial magnitudes of Fourier transform are obtained. In particular, we consider structured illuminated patterns in holography and find that noninteger values used in designing such patterns often yield better reconstruction than the conventional integer-valued ones. Furthermore, we demonstrate theoretically and numerically that three diffracted sets of (complete) magnitude data are sufficient to recover the object. To compensate for incomplete information, we incorporate a total variation regularization a priori to guarantee that the reconstructed image satisfies some desirable properties. The proposed model can be solved efficiently by an alternative directional multiplier method with provable convergence. Numerical experiments valid...

Autocalibration and Uncalibrated Reconstruction of Shape from Defocus

Most algorithms for reconstructing shape from defocus assume that the images are obtained with a camera that has been previously calibrated so that the aperture, focal plane, and focal length are known. In this manuscript we characterize the set of scenes that can be reconstructed from defocused images regardless of calibration parameters. In lack of knowledge about the camera or about the scene, reconstruction is possible only up to an equivalence class that is described analytically. When weak knowledge about the scene is available, however, we show how it can be exploited in order to auto-calibrate the imaging device. This includes imaging a slanted plane or generic assumptions on the restoration of the deblurred images.

Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P

VIDEO STABILIZATION OF ATMOSPHERIC TURBULENCE DISTORTION

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Spiral Scanning and Encased Cantilevers for High Spatial and Temporal Resolution in Atomic Force Microscopy

ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P