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In recent years, many papers have been devoted to the topic of balanced multiwavelets, namely, multiwavelet bases which are especially designed to avoid the prefiltering step in the implementation of the multiwavelet transform. In this work, we give a simple algebraic proof of how scalar wavelets can be reinterpreted as the most natural balanced multiwavelets, which maintain the good properties of the wavelet bases they come from. We then show how these new bases can be successfully used to apply matrix thresholding for the denoising of images corrupted by Gaussian noise. In fact, this new approach discovers a balanced matrix nature in Daubechies bases, hence obtaining better numerical results with respect to those achieved via scalar thresholding. In particular, this reinterpretation of scalar wavelets as balanced multiwavelets allows us to successfully use the thresholding filters, previously introduced in the scalar case, in a matrix setting. [ABSTRACT FROM AUTHOR]

Abstract: In this work we describe a method for removing Gaussian noise from digital images, based on the combination of the wavelet packet transform and the principal component analysis. In particular, since the aim of denoising is to retain the energy of the signal while discarding the energy of the noise, our basic idea is to construct powerful tailored filters by applying the Karhunen–Loéve transform in the wavelet packet domain, thus obtaining a compaction of the signal energy into a few principal components, while the noise is spread over all the transformed coefficients. This allows us to act with a suitable shrinkage function on these new coefficients, removing the noise without blurring the edges and the important characteristics of the images. The results of a large numerical experimentation encourage us to keep going in this direction with our studies. [Copyright &y& Elsevier]

When working with nonlinear filtering algorithms for image denoising problems, there are two crucial aspects, namely, the choice of the thresholding parameter λ and the use of a proper filter function. Both greatly influence the quality of the resulting denoised image. In this paper we propose two new filters, which are a piecewise quadratic and an exponential function of λ, respectively, arid we show how they can be successfully used instead of the classical Donoho and Johnstone''s Soft thresholding filter. We exploit the increased regularity and flexibility of the new filters to improve the quality of the final results. Moreover, we prove that our filtered approximation is a near-minimizer of the functional which has to be minimized to solve the denoising problem. We also show that the quadratic filter, due to its shape, yields good results if we choose λ as the Donoho and Johnstone universal threshold, while the exponential one is more suitable if we use the recently proposed H-curve criterion. Encouraging results in extensive numerical experiments on several test images confirm the effectiveness of our proposal. [Copyright &y& Elsevier]

Object detection and recognition are challenging computer vision tasks receiving great attention due to the large number of applications. This work focuses on the detection/recognition of products in supermarket shelves; this framework has a number of practical applications such as providing additional product/price information to the user or guiding visually impaired customers during shopping. The automatic creation of planograms (i.e., actual layout of products on shelves) is also useful for commercial analysis and management of large stores. Although in many object detection/recognition contexts it can be assumed that training images are representative of the real operational conditions, in our scenario such assumption is not realistic because the only training images available are acquired in well-controlled conditions. This gap between the training and test data makes the object detection and recognition tasks far more complex and requires very robust techniques. In this paper we prove that good results can be obtained by exploiting color and texture information in a multi-stage process: pre-selection, fine-selection and post processing. For fine-selection we compared a classical Bag of Words technique with a more recent Deep Neural Networks approach and found interesting outcomes. Extensive experiments on datasets of varying complexity are discussed to highlight the main issues characterizing this problem, and to guide toward the practical development of a real application. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering a sparse signal when its nonzero coefficients tend to cluster into blocks, whose number, dimension and position are unknown. We refer to this problem as blind cluster structured sparse recovery . For its solution, differently from the existing methods that consider the problem in a statistical context, we propose a deterministic neighborhood based approach characterized by the use both of a nonconvex, nonseparable sparsity inducing function and of a penalized version of the iterative ℓ 1 reweighted method. Despite the high nonconvexity of the approach, a suitable integration of these building elements led to the development of MB-NFCS ( Model Based Nonlinear Filtering for Compressed Sensing ), an iterative fast, self-adaptive, and efficient algorithm that, without requiring any information on the sparsity pattern, adjusts at each iteration the action of the sparsity inducing function in order to strongly encourage the emerging cluster structure. The effectiveness of the proposed approach is demonstrated by a large set of numerical experiments that show the superior performance of MB-NFCS to the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of sparse signal recovery from a lower number of measurements than those requested by the classical compressed sensing theory. This problem is formalized as a constrained minimization problem, where the objective function is nonconvex and singular at the origin. Several algorithms have been recently proposed, which rely on iterative reweighting schemes, that produce better estimates at each new minimization step. Two such methods are iterative reweighted l 2 and l 1 minimization that have been shown to be effective and general, but very computationally demanding. The main contribution of this paper is the proposal of the algorithm WNFCS, where the reweighted schemes represent the core of a penalized approach to the solution of the constrained nonconvex minimization problem. The algorithm is fast, and succeeds in exactly recovering a sparse signal from a smaller number of measurements than the l 1 minimization and in a shorter time. WNFCS is very general, since it represents an algorithmic framework that can easily be adapted to different reweighting strategies and nonconvex objective functions. Several numerical experiments and comparisons with some of the most recent nonconvex minimization algorithms confirm the capabilities of the proposed algorithm. [Copyright &y& Elsevier]

The problem of high-resolution image volume reconstruction from reduced frequency acquisition sequences has drawn significant attention from the scientific community because of its practical importance in medical diagnosis. To address this issue, several reconstruction strategies have been recently proposed, which aim to recover the missing information either by exploiting the spatio-temporal correlations of the image series, or by imposing suitable constraints on the reconstructed image volume. The main contribution of this paper is to combine both these strategies in a compressed sensing framework by exploiting the gradient sparsity of the image volume. The resulting constrained 3D minimization problem is then solved using a penalized forward–backward splitting approach that leads to a convergent iterative two-step procedure. In the first step, the updating rule accords with the sequential nature of the data acquisitions, in the second step a truly 3D filtering strategy exploits the spatio-temporal correlations of the image sequences. The resulting NFCS-3D algorithm is very general and suitable for several kinds of medical image reconstruction problems. Moreover, it is fast, stable and yields very good reconstructions, even in the case of highly undersampled image sequences. The results of several numerical experiments highlight the optimal performance of the proposed algorithm and confirm that it is competitive with state of the art algorithms. [ABSTRACT FROM AUTHOR]

Compressed sensing is a new paradigm for signal recovery and sampling. It states that a relatively small number of linear measurements of a sparse signal can contain most of its salient information and that the signal can be exactly reconstructed from these highly incomplete observations. The major challenge in practical applications of compressed sensing consists in providing efficient, stable and fast recovery algorithms which, in a few seconds, evaluate a good approximation of a compressible image from highly incomplete and noisy samples. In this paper, we propose to approach the compressed sensing image recovery problem using adaptive nonlinear filtering strategies in an iterative framework, and we prove the convergence of the resulting two-steps iterative scheme. The results of several numerical experiments confirm that the corresponding algorithm possesses the required properties of efficiency, stability and low computational cost and that its performance is competitive with those of the state of the art algorithms. [ABSTRACT FROM AUTHOR]

The problem of recovering sparse signals and sparse gradient signals from a small collection of linear measurements is one that arises naturally in many scientific fields. The recently developed Compressed Sensing Framework states that such problems can be solved by searching for the signal of minimum L1-norm, or minimum Total Variation, that satisfies the given acquisition constraints. While L1 optimization algorithms, based on Linear Programming techniques, are highly effective at generating excellent signal reconstructions, their complexity is still too high and renders them impractical for many real applications. In this paper, we propose a novel approach to solve the L1 optimization problems, based on the use of suitable nonlinear filters widely applied for signal and image denoising. The corresponding algorithm has two main advantages: low computational cost and reconstruction capabilities similar to those of Linear Programming optimization methods. We illustrate the effectiveness of the proposed approach with many numerical examples and comparisons. [ABSTRACT FROM AUTHOR]

In this paper we present a new approach to rank and select keypoints based on their saliency for object detection and matching under moderate viewpoint and lighting changes. Saliency is defined in terms of detectability, repeatability and distinctiveness by considering both the keypoint strength (as returned by the detector algorithm) and the associated local descriptor discriminating power. Our experiments prove that selecting a small amount of available keypoints (e.g., 10%) not only boosts efficiency but can also lead to better detection/matching accuracy thus making the proposed method attractive for real-time applications (e.g., augmented reality). [ABSTRACT FROM AUTHOR]