Abstract. We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or q-linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed.

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Abstract.We extend the alternating minimization algorithm recently proposed in [38,39] to the case of recovering blurry multichannel (color) images corrupted by impulsive rather than Gaussian noise. The algorithm minimizes the sum of a multichannel extension of total variation (TV), either isotropic or anisotropic, and a data fidelity term measured in the L 1 -norm. We derive the algorithm by applying the well-known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and global q-linear convergence. Under periodic boundary conditions, the main computational requirements of the algorithm are fast Fourier transforms and a low-complexity Gaussian elimination procedure. Numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm. In addition, it is numerically compared to an algorithm recently proposed in [20] that uses a linear program and an interior point method for recovering grayscale images.

Abstract. The nuclear norm is widely used to induce low-rank solutions for many optimization problems with matrix variables. Recently, it has been shown that the augmented Lagrangian method (ALM) and the alternating direction method (ADM) are very efficient for many convex programming problems arising from various applications, provided that the resulting subproblems are sufficiently simple to have closed-form solutions. In this paper, we are interested in the application of the ALM and the ADM for some nuclear norm involved minimization problems. When the resulting subproblems do not have closed-form solutions, we propose to linearize these subproblems such that closed-form solutions of these linearized subproblems can be easily derived. Global convergence of these linearized ALM and ADM are established under standard assumptions. Finally, we verify the effectiveness and efficiency of these new methods by some numerical experiments.

Abstract. We generalize the alternating minimization algorithm recently proposed in [32] to efficiently solve a general, edge-preserving, variational model for recovering multichannel images degraded by within-and cross-channel blurs, as well as additive Gaussian noise. This general model allows the use of localized weights and higher-order derivatives in regularization, and includes a multichannel extension of total variation (MTV) regularization as a special case. In the MTV case, we show that the model can be derived from an extended half-quadratic transform of Geman and Yang [14]. For color images with three channels and when applied to the MTV model (either locally weighted or not), the per-iteration computational complexity of this algorithm is dominated by nine fast Fourier transforms. We establish strong convergence results for the algorithm including finite convergence for some variables and fast q-linear convergence for the others. Numerical results on various types of blurs are presented to demonstrate the performance of our algorithm compared to that of the MATLAB deblurring functions. We also present experimental results on regularization models using weighted MTV and higher-order derivatives to demonstrate improvements in image quality provided by these models over the plain MTV model.

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This paper shows how to use model checking to find serious errors in file systems. Model checking is a formal verification technique tuned for finding corner-case errors by comprehensively exploring the state spaces defined by a system. File systems have two dynamics that make them attractive for such an approach. First, their errors are some of the most serious, since they can destroy persistent data and lead to unrecoverable corruption. Second, traditional testing needs an impractical, exponential number of test cases to check that the system will recover if it crashes at any point during execution. Model checking employs a variety of state-reducing techniques that allow it to explore such vast state spaces efficiently.We built a system, FiSC, for model checking file systems. We applied it to three widely-used, heavily-tested file systems: ext3 [13], JFS [21], and ReiserFS [27]. We found serious bugs in all of them, 32 in total. Most have led to patches within a day of diagnosis. For each file system, FiSC found demonstrable events leading to the unrecoverable destruction of metadata and entire directories, including the file system root directory "/".

Fuzzing has become the de facto standard technique for finding software vulnerabilities. However, even state-of-theart fuzzers are not very efficient at finding hard-to-trigger software bugs. Most popular fuzzers use evolutionary guidance to generate inputs that can trigger different bugs. Such evolutionary algorithms, while fast and simple to implement, often get stuck in fruitless sequences of random mutations. Gradient-guided optimization presents a promising alternative to evolutionary guidance. Gradient-guided techniques have been shown to significantly outperform evolutionary algorithms at solving high-dimensional structured optimization problems in domains like machine learning by efficiently utilizing gradients or higher-order derivatives of the underlying function.However, gradient-guided approaches are not directly applicable to fuzzing as real-world program behaviors contain many discontinuities, plateaus, and ridges where the gradientbased methods often get stuck. We observe that this problem can be addressed by creating a smooth surrogate function approximating the target program's discrete branching behavior. In this paper, we propose a novel program smoothing technique using surrogate neural network models that can incrementally learn smooth approximations of a complex, real-world program's branching behaviors. We further demonstrate that such neural network models can be used together with gradient-guided input generation schemes to significantly increase the efficiency of the fuzzing process.Our extensive evaluations demonstrate that NEUZZ significantly outperforms 10 state-of-the-art graybox fuzzers on 10 popular real-world programs both at finding new bugs and achieving higher edge coverage. NEUZZ found 31 previously unknown bugs (including two CVEs) that other fuzzers failed to find in 10 real-world programs and achieved 3X more edge coverage than all of the tested graybox fuzzers over 24 hour runs. Furthermore, NEUZZ also outperformed existing fuzzers on both LAVA-M and DARPA CGC bug datasets.