Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms

@article{Carmi2010MethodsFS,
  title={Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms},
  author={Avishy Carmi and Pini Gurfil and Dimitri Kanevsky},
  journal={IEEE Transactions on Signal Processing},
  year={2010},
  volume={58},
  pages={2405-2409}
}
We present two simple methods for recovering sparse signals from a series of noisy observations. The theory of compressed sensing (CS) requires solving a convex constrained minimization problem. We propose solving this optimization problem by two algorithms that rely on a Kalman filter (KF) endowed with a pseudo-measurement (PM) equation. Compared to a recently-introduced KF-CS method, which involves the implementation of an auxiliary CS optimization algorithm (e.g., the Dantzig selector), our… 

Figures from this paper

Extended Compressed Sensing : Filtering Inspired Methods for Sparse Signal Recovery and Their Nonlinear Variants
TLDR
The extended Baum-Welch (EBW), a popular algorithm for discriminative training of s peech models, is amended here for recovery of normalized sparse signals and has a prominent advantage over the nonlinear exte nsions of the KF-based algorithms which rely on validity of linearization.
Kalman filtering for compressed sensing
TLDR
This work provides a rigorous treatment of the CSKF algorithm which is concluded with an upper bound on the discrepancy between the exact (in the Bayesian sense) and the approximate solutions.
Convex feasibility modeling and projection methods for sparse signal recovery
Distributed sparse signal estimation in sensor networks using H∞-consensus filtering
This paper is concerned with the sparse signal recovery problem in sensor networks, and the main purpose is to design a filter for each sensor node to estimate a sparse signal sequence using the
Compressive system identification: Sequential methods and entropy bounds
  • A. Carmi
  • Computer Science, Mathematics
    Digit. Signal Process.
  • 2013
Sparse and low rank signal recovery with partial knowledge
TLDR
A novel “online” RPCA algorithm based on the recently introduced Recursive Projected Compressive Sensing is developed and studied and its correctness result is derived, which shows that modified-PCP indeed requires significantly weaker incoherence assumptions than PCP, when the available subspace knowledge is accurate.
Convex Feasibility Methods for Compressed Sensing
TLDR
This work proposes to transform the problem of compressed sensing into a convex feasibility problem (CFP), and solve it using subgradient projection methods, which are iterative, fast, robust and convergent schemes for solving CFPs.
Compressive System Identification
The first part of this chapter presents a novel Kalman filtering-based method for estimating the coefficients of sparse, or more broadly, compressible autoregressive models using fewer observations
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
Kalman filtered Compressed Sensing
  • N. Vaswani
  • Computer Science
    2008 15th IEEE International Conference on Image Processing
  • 2008
TLDR
This work considers the problem of reconstructing time sequences of spatially sparse signals from a limited number of linear "incoherent" measurements, in real-time, and uses Compressed Sensing to estimate the support set of the initial signal's transform vector.
Exact Reconstruction of Sparse Signals via Nonconvex Minimization
  • R. Chartrand
  • Computer Science
    IEEE Signal Processing Letters
  • 2007
TLDR
It is shown that by replacing the lscr1 norm with theLscrp norm, exact reconstruction is possible with substantially fewer measurements, and a theorem in this direction is given.
ABCS : Approximate Bayesian Compressed Sensing
TLDR
A random field-based classifier util izing the approximate Bayesian CS scheme is shown to attain a zero error rate when applied to fMRI classifi cation.
On Kalman Filtering With Nonlinear Equality Constraints
TLDR
This paper proposes a new method that utilizes the projection method twice-once to constrain the entire distribution and once to Constrain the statistics of the distribution, and illustrates these algorithms in a tracking system that uses unit quaternions to encode orientation.
Sparse MRI: The application of compressed sensing for rapid MR imaging
TLDR
Practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference and demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin‐echo brain imaging and 3D contrast enhanced angiography.
Compressive sampling
TLDR
Some of the key mathematical insights underlying this new sampling theory are provided, and some of the interactions between compressive sampling and other fields such as statistics, information theory, coding theory, and theoretical computer science are explained.
Compressed sensing in dynamic MRI
TLDR
Given sufficient data sparsity and base signal‐to‐noise ratio (SNR), CS is demonstrated to result in improved temporal fidelity compared to k‐t BLAST reconstructions for the example data sets used in this work.
Atomic Decomposition by Basis Pursuit
TLDR
Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TLDR
It is shown how one can reconstruct a piecewise constant object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.
Regression Shrinkage and Selection via the Lasso
TLDR
A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
...
1
2
...