Searcharxiv⌕ Search

arXiv subjects

Pier Luigi Dragotti

Publications and source records attributed to Pier Luigi Dragotti.

47 records · Page 3Linked to original sources

Privacy-Aware Location Sharing with Deep Reinforcement Learning

Location-based services (LBSs) have become widely popular. Despite their utility, these services raise concerns for privacy since they require sharing location information with untrusted third parties. In this work, we study privacy-utility trade-off in location sharing mechanisms. Existing approaches are mainly focused on privacy of sharing a single location or myopic location trace privacy; neither of them taking into account the temporal correlations between the past and current locations. Although these methods preserve the privacy for the current time, they may leak significant amount of information at the trace level as the adversary can exploit temporal correlations in a trace. We propose an information theoretically optimal privacy preserving location release mechanism that takes temporal correlations into account. We measure the privacy leakage by the mutual information between the user's true and released location traces. To tackle the history-dependent mutual information minimization, we reformulate the problem as a Markov decision process (MDP), and solve it using asynchronous actor-critic deep reinforcement learning (RL).

cs.IT↗

Privacy-cost trade-off in a smart meter system with a renewable energy source and a rechargeable battery

We study the privacy-cost trade-off in a smart meter (SM) system with a renewable energy source (RES) and a finite-capacity rechargeable battery (RB). Privacy is measured by the mutual information rate between the energy demand and the energy received from the grid, where the latter also determines the cost, and hence, reported by the SM to the utility provider (UP). We consider a renewable energy generation process that fully charges the RB at random time instants, and its realization is assumed to be known also by the UP. We reformulate the problem as a Markov decision process (MDP), and solve it by dynamic programming (DP) to design battery charging and discharging policies that minimize a linear combination of the privacy leakage and energy cost. We also propose a lower bound and two alternative low-complexity energy management policies, one of which is shown numerically to perform close to the MDP solution.

cs.IT↗

Multimodal Image Super-resolution via Joint Sparse Representations induced by Coupled Dictionaries

Real-world data processing problems often involve various image modalities associated with a certain scene, including RGB images, infrared images or multi-spectral images. The fact that different image modalities often share certain attributes, such as certain edges, textures and other structure primitives, represents an opportunity to enhance various image processing tasks. This paper proposes a new approach to construct a high-resolution (HR) version of a low-resolution (LR) image given another HR image modality as reference, based on joint sparse representations induced by coupled dictionaries. Our approach, which captures the similarities and disparities between different image modalities in a learned sparse feature domain in \emph{lieu} of the original image domain, consists of two phases. The coupled dictionary learning phase is used to learn a set of dictionaries that couple different image modalities in the sparse feature domain given a set of training data. In turn, the coupled super-resolution phase leverages such coupled dictionaries to construct a HR version of the LR target image given another related image modality. One of the merits of our sparsity-driven approach relates to the fact that it overcomes drawbacks such as the texture copying artifacts commonly resulting from inconsistency between the guidance and target images. Experiments on real multimodal images demonstrate that incorporating appropriate guidance information via joint sparse representation induced by coupled dictionary learning brings notable benefits in the super-resolution task with respect to the state-of-the-art. Of particular relevance, the proposed approach also demonstrates better robustness than competing deep-learning-based methods in the presence of noise.

cs.CV↗

Splines and Wavelets on Circulant Graphs

We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the design of vertex-localized and critically-sampled higher-order graph (e-)spline wavelet filterbanks, which can reproduce and annihilate classes of (exponential) polynomial signals on circulant graphs. In addition, we discuss similarities and analogies of the detected properties and resulting constructions with splines and spline wavelets in the Euclidean domain. Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions. In particular, we proceed to show how the use of graph products facilitates a multi-dimensional extension of the proposed constructions and properties.

cs.DM↗

Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, and subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.

cs.DM↗

A Sampling Framework for Solving Physics-driven Inverse Source Problems

Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain results in sampling and approximation theory, we present a new framework for solving a class of inverse source problems for physical fields governed by linear partial differential equations. Specifically, we demonstrate that the unknown field sources can be recovered from a sequence of, so called, generalised measurements by using multidimensional frequency estimation techniques. Next we show that---for physics-driven fields---this sequence of generalised measurements can be estimated by computing a linear weighted-sum of the sensor measurements; whereby the exact weights (of the sums) correspond to those that reproduce multidimensional exponentials, when used to linearly combine translates of a particular prototype function related to the Green's function of our underlying field. Explicit formulae are then derived for the sequence of weights, that map sensor samples to the exact sequence of generalised measurements when the Green's function satisfies the generalised Strang-Fix condition. Otherwise, the same mapping yields a close approximation of the generalised measurements. Based on this new framework we develop practical, noise robust, sensor network strategies for solving the inverse source problem, and then present numerical simulation results to verify their performance.

cs.IT↗

Sparse Representation in Fourier and Local Bases Using ProSparse: A Probabilistic Analysis

Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation problem when the underlying dictionary is the union of a Vandermonde matrix and a banded matrix. Unlike our previous work which establishes deterministic (worst-case) sparsity bounds for ProSparse to succeed, this paper presents a probabilistic average-case analysis of the algorithm. Based on a generating-function approach, closed-form expressions for the exact success probabilities of ProSparse are given. The success probabilities are also analyzed in the high-dimensional regime. This asymptotic analysis characterizes a sharp phase transition phenomenon regarding the performance of the algorithm.

cs.IT↗

Deep De-Aliasing for Fast Compressive Sensing MRI

Fast Magnetic Resonance Imaging (MRI) is highly in demand for many clinical applications in order to reduce the scanning cost and improve the patient experience. This can also potentially increase the image quality by reducing the motion artefacts and contrast washout. However, once an image field of view and the desired resolution are chosen, the minimum scanning time is normally determined by the requirement of acquiring sufficient raw data to meet the Nyquist-Shannon sampling criteria. Compressive Sensing (CS) theory has been perfectly matched to the MRI scanning sequence design with much less required raw data for the image reconstruction. Inspired by recent advances in deep learning for solving various inverse problems, we propose a conditional Generative Adversarial Networks-based deep learning framework for de-aliasing and reconstructing MRI images from highly undersampled data with great promise to accelerate the data acquisition process. By coupling an innovative content loss with the adversarial loss our de-aliasing results are more realistic. Furthermore, we propose a refinement learning procedure for training the generator network, which can stabilise the training with fast convergence and less parameter tuning. We demonstrate that the proposed framework outperforms state-of-the-art CS-MRI methods, in terms of reconstruction error and perceptual image quality. In addition, our method can reconstruct each image in 0.22ms--0.37ms, which is promising for real-time applications.

cs.CV↗

A Novel Semantics and Feature Preserving Perspective for Content Aware Image Retargeting

There is an increasing requirement for efficient image retargeting techniques to adapt the content to various forms of digital media. With rapid growth of mobile communications and dynamic web page layouts, one often needs to resize the media content to adapt to the desired display sizes. For various layouts of web pages and typically small sizes of handheld portable devices, the importance in the original image content gets obfuscated after resizing it with the approach of uniform scaling. Thus, there occurs a need for resizing the images in a content aware manner which can automatically discard irrelevant information from the image and present the salient features with more magnitude. There have been proposed some image retargeting techniques keeping in mind the content awareness of the input image. However, these techniques fail to prove globally effective for various kinds of images and desired sizes. The major problem is the inefficiency of these algorithms to process these images with minimal visual distortion while also retaining the meaning conveyed from the image. In this dissertation, we present a novel perspective for content aware image retargeting, which is well implementable in real time. We introduce a novel method of analysing semantic information within the input image while also maintaining the important and visually significant features. We present the various nuances of our algorithm mathematically and logically, and show that the results prove better than the state-of-the-art techniques.

cs.GR↗

On Sparse Representation in Fourier and Local Bases

We consider the classical problem of finding the sparse representation of a signal in a pair of bases. When both bases are orthogonal, it is known that the sparse representation is unique when the sparsity $K$ of the signal satisfies $K<1/μ(D)$, where $μ(D)$ is the mutual coherence of the dictionary. Furthermore, the sparse representation can be obtained in polynomial time by Basis Pursuit (BP), when $K<0.91/μ(D)$. Therefore, there is a gap between the unicity condition and the one required to use the polynomial-complexity BP formulation. For the case of general dictionaries, it is also well known that finding the sparse representation under the only constraint of unicity is NP-hard. In this paper, we introduce, for the case of Fourier and canonical bases, a polynomial complexity algorithm that finds all the possible $K$-sparse representations of a signal under the weaker condition that $K<\sqrt{2} /μ(D)$. Consequently, when $K<1/μ(D)$, the proposed algorithm solves the unique sparse representation problem for this structured dictionary in polynomial time. We further show that the same method can be extended to many other pairs of bases, one of which must have local atoms. Examples include the union of Fourier and local Fourier bases, the union of discrete cosine transform and canonical bases, and the union of random Gaussian and canonical bases.

cs.IT↗

Transform coder identification based on quantization footprints and lattice theory

Transform coding is routinely used for lossy compression of discrete sources with memory. The input signal is divided into N-dimensional vectors, which are transformed by means of a linear mapping. Then, transform coefficients are quantized and entropy coded. In this paper we consider the problem of identifying the transform matrix as well as the quantization step sizes. We study the challenging case in which the only available information is a set of P transform decoded vectors. We formulate the problem in terms of finding the lattice with the largest determinant that contains all observed vectors. We propose an algorithm that is able to find the optimal solution and we formally study its convergence properties. Our analysis shows that it is possible to identify successfully both the transform and the quantization step sizes when P >= N + d where d is a small integer, and the probability of failure decreases exponentially to zero as P - N increases.

cs.IT↗