Publications by Pier Luigi Dragotti

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Linear transforms and expansions are fundamental mathematical tools of signal processing. In particular, the wavelet transform has played an important role in several signal processing tasks, compression being a prime example. A signal can be represented in a basis or a frame. Frames, which are an extension of bases to overcomplete sets of vectors, are sometimes preferred to bases because of their greater design freedom and recently they have had an important impact in signal processing. This thesis focuses

Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom ...

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

The Karhunen–Loève transform (KLT) is a key ele- ment of many signal processing and communication tasks. Many recent applications involve distributed signal processing, where it is not generally possible to apply the KLT to the entire signal; rather, the K ...

In this paper, we discuss a framework for the distributed compression of vector sources, based on our previous work on distributed transform coding. In particular, our goal is to develop a strategy of first applying a suitable distributed Karhunen-Loeve transform, whereafter each component can be andled by standard distributed compression techniques. In the present paper, we first study the scenario where all but one terminal furnish a noisy approximation of their observation. For the case where the underly

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

In this letter, we present a possible extension of the theory of sampling signals with finite rate of innovation (FRI) to the case of multichannel acquisition systems. The essential issue of a multichannel system is that each channel introduces different unknown delays and gains that need to be estimated for the calibration of the channels. We pose both the synchronization stage and the signal reconstruction stage as a parametric estimation problem and demonstrate that a simultaneous exact synchronization o

In recent years, wavelet-based algorithms have been successful in different signal processing tasks. The wavelet trans- form is a powerful tool because it manages to represent both tran- sient and stationary behaviors of a signal with few transform coeffi- cients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. In this paper, we study the dependency across scales of the wavelet coefficients generated by discontinuities. We start by showing t

This paper presents a rigorous assessment of natural frequencies associated with fault-originated travelling waves in power networks, factoring in the presence of multiple junctions and branches. The proposed assessment exploits the Baum-Liu-Tesche (BLT) e ...

Consider a diffusion field induced by a finite number of localized and instantaneous sources. In this paper, we study the problem of estimating these sources (including their intensities, spatial locations, and activation time) from the spatiotemporal samp ...

Multiple description (MD) coding is a source coding technique for information transmission over unreliable networks. In MD coding, the coder generates several different descriptions of the same signal and the decoder can produce a useful reconstruction of the source with any received subset of these descriptions. In this paper, we study the problem of MD coding of stationary Gaussian sources with memory. First, we compute an approximate MD rate distortion region for these sources, which we prove to be asymp

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymp- totic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join sch ...

The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental ques- tions concerns the sufficiency of discrete approximations in time, space, ...

The Karhunen-Loeve transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Many recent applications involve {\em distributed} signal processing where it is not generally possible to apply the KLT to the signal; rather, the KLT must be approximated in a distributed fashion. This paper investigates such distributed approximations to the KLT. First, we present explicit solutions to special cases, including a partial KLT (where only a subset of

Consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, nonuniform splines or piecewise polynomials, and call the number of degrees of freedom per unit ...

The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental questions concerns the sufficiency of discrete approximations in time, space, an ...

We study the problem of multiple description (MD) coding of stationary Gaussian sources with memory. First, we compute an approximate rate distortion region for these sources, which we prove to be asymptotically tight at high rates: this region generalizes the standard MD rate distortion region for memoryless sources. Then we develop an algorithm for the design of optimal biorthogonal filter banks for MD coding. Finally. We present some experimental results, where we measure the deviation from optimality of

The Karhunen-Loeve transform is a key element of many signal processing tasks, including classification and compression. In this paper, we consider distributed signal processing scenarios with limited communication between correlated sources, and we investigate a distributed Karhunen-Loeve transform (KLT). In particular, a partial KLT (where only a subset of sources are observed) and a conditional KLT (where some sources act as side information) are posed and solved in a rate-distortion sense. The partial K

In this paper, we consider classes of not bandlimited signals, namely, streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution structure of the wavelet transform, these new sampling theorems naturally lead to the development of a new resolution enhancement algo- rithm based on wavelet footprints [2]. Preliminary results show the potentiality of this algorithm.

Super-resolution algorithms combine multiple low resolution images into a single high resolution image. They have received a lot of attention recently in various application domains such as HDTV, satellite imaging, and video surveillance. These techniques ...

Pier Luigi Dragotti

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Wavelet footprints and frames for signal processing and communication

Exact Local Reconstruction Algorithms for Signals with Finite Rate of Innovation

Directionlets: Anisotropic Multidirectional representation with separable filtering

The Distributed Karhunen-Loève Transform

On Compression Using the Distributed Karhunen-Loeve Transform

Low-Rate Reduced Complexity Image Compression using Directionlets

Multichannel Sampling of Signals With Finite Rate of Innovation

Wavelet Footprints: Theory, Algorithms and Applications

Rigorous Assessment of Natural Frequencies of Fault-Originated Travelling Waves

Localization of Diffusive Sources Using Spatiotemporal Measurements

Optimal Filter Banks for Multiple Description Coding: Analysis and Synthesis

Rate-Distortion Optimized Tree-Structured Compression Algorithms for Piecewise Polynomial Images

Sensing and communication with and without bits

The distributed Karhunen-Loeve transform

Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix

Sensing reality and communicating bits: A dangerous liaison

Analysis of optimal filter banks for multiple description coding

The distributed Karhunen-Loeve transform

Wavelet and footprint sampling of signals with a finite rate of innovation

Subspace-Based Methods for Image Registration and Super-Resolution