Adaptive Image Denoising by Targeted Databases

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains only relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images and face images. Experimental results show the superiority of the new algorithm over existing methods.Comment: 15 pages, 13 figures, 2 tables, journa

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Rapid three-dimensional multiparametric MRI with quantitative transient-state imaging

Novel methods for quantitative, transient-state multiparametric imaging are increasingly being demonstrated for assessment of disease and treatment efficacy. Here, we build on these by assessing the most common Non-Cartesian readout trajectories (2D/3D radials and spirals), demonstrating efficient anti-aliasing with a k-space view-sharing technique, and proposing novel methods for parameter inference with neural networks that incorporate the estimation of proton density. Our results show good agreement with gold standard and phantom references for all readout trajectories at 1.5T and 3T. Parameters inferred with the neural network were within 6.58% difference from the parameters inferred with a high-resolution dictionary. Concordance correlation coefficients were above 0.92 and the normalized root mean squared error ranged between 4.2% - 12.7% with respect to gold-standard phantom references for T1 and T2. In vivo acquisitions demonstrate sub-millimetric isotropic resolution in under five minutes with reconstruction and inference times < 7 minutes. Our 3D quantitative transient-state imaging approach could enable high-resolution multiparametric tissue quantification within clinically acceptable acquisition and reconstruction times.Comment: 43 pages, 12 Figures, 5 Table

Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the \emph{tightest} lower/upper bound on Euclidean distances when each data object is potentially compressed using a different set of orthonormal coefficients. Our technique leads to tighter distance estimates, which translates into more accurate search, learning and mining operations \textit{directly} in the compressed domain. We formulate the problem of estimating lower/upper distance bounds as an optimization problem. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an \emph{exact} solution to the problem. The suggested solution provides the tightest estimation of the $L_2$-norm or the correlation. We show that typical data-analysis operations, such as k-NN search or k-Means clustering, can operate more accurately using the proposed compression and distance reconstruction technique. We compare it with many other prevalent compression and reconstruction techniques, including random projections and PCA-based techniques. We highlight a surprising result, namely that when the data are highly sparse in some basis, our technique may even outperform PCA-based compression. The contributions of this work are generic as our methodology is applicable to any sequential or high-dimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD

Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view

Is there anything new to say about SIFT matching?

SIFT is a classical hand-crafted, histogram-based descriptor that has deeply influenced research on image matching for more than a decade. In this paper, a critical review of the aspects that affect SIFT matching performance is carried out, and novel descriptor design strategies are introduced and individually evaluated. These encompass quantization, binarization and hierarchical cascade filtering as means to reduce data storage and increase matching efficiency, with no significant loss of accuracy. An original contextual matching strategy based on a symmetrical variant of the usual nearest-neighbor ratio is discussed as well, that can increase the discriminative power of any descriptor. The paper then undertakes a comprehensive experimental evaluation of state-of-the-art hand-crafted and data-driven descriptors, also including the most recent deep descriptors. Comparisons are carried out according to several performance parameters, among which accuracy and space-time efficiency. Results are provided for both planar and non-planar scenes, the latter being evaluated with a new benchmark based on the concept of approximated patch overlap. Experimental evidence shows that, despite their age, SIFT and other hand-crafted descriptors, once enhanced through the proposed strategies, are ready to meet the future image matching challenges. We also believe that the lessons learned from this work will inspire the design of better hand-crafted and data-driven descriptors