9,975 research outputs found
Communications-Inspired Projection Design with Application to Compressive Sensing
We consider the recovery of an underlying signal x \in C^m based on
projection measurements of the form y=Mx+w, where y \in C^l and w is
measurement noise; we are interested in the case l < m. It is assumed that the
signal model p(x) is known, and w CN(w;0,S_w), for known S_W. The objective is
to design a projection matrix M \in C^(l x m) to maximize key
information-theoretic quantities with operational significance, including the
mutual information between the signal and the projections I(x;y) or the Renyi
entropy of the projections h_a(y) (Shannon entropy is a special case). By
capitalizing on explicit characterizations of the gradients of the information
measures with respect to the projections matrix, where we also partially extend
the well-known results of Palomar and Verdu from the mutual information to the
Renyi entropy domain, we unveil the key operations carried out by the optimal
projections designs: mode exposure and mode alignment. Experiments are
considered for the case of compressive sensing (CS) applied to imagery. In this
context, we provide a demonstration of the performance improvement possible
through the application of the novel projection designs in relation to
conventional ones, as well as justification for a fast online projections
design method with which state-of-the-art adaptive CS signal recovery is
achieved.Comment: 25 pages, 7 figures, parts of material published in IEEE ICASSP 2012,
submitted to SIIM
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
The affine rank minimization problem consists of finding a matrix of minimum
rank that satisfies a given system of linear equality constraints. Such
problems have appeared in the literature of a diverse set of fields including
system identification and control, Euclidean embedding, and collaborative
filtering. Although specific instances can often be solved with specialized
algorithms, the general affine rank minimization problem is NP-hard. In this
paper, we show that if a certain restricted isometry property holds for the
linear transformation defining the constraints, the minimum rank solution can
be recovered by solving a convex optimization problem, namely the minimization
of the nuclear norm over the given affine space. We present several random
ensembles of equations where the restricted isometry property holds with
overwhelming probability. The techniques used in our analysis have strong
parallels in the compressed sensing framework. We discuss how affine rank
minimization generalizes this pre-existing concept and outline a dictionary
relating concepts from cardinality minimization to those of rank minimization
A distributed optimization framework for localization and formation control: applications to vision-based measurements
Multiagent systems have been a major area of research for the last 15 years. This interest has been motivated by tasks that can be executed more rapidly in a collaborative manner or that are nearly impossible to carry out otherwise. To be effective, the agents need to have the notion of a common goal shared by the entire network (for instance, a desired formation) and individual control laws to realize the goal. The common goal is typically centralized, in the sense that it involves the state of all the agents at the same time. On the other hand, it is often desirable to have individual control laws that are distributed, in the sense that the desired action of an agent depends only on the measurements and states available at the node and at a small number of neighbors. This is an attractive quality because it implies an overall system that is modular and intrinsically more robust to communication delays and node failures
- …