102 research outputs found
Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors
The Kaczmarz algorithm is popular for iteratively solving an overdetermined
system of linear equations. The traditional Kaczmarz algorithm can approximate
the solution in few sweeps through the equations but a randomized version of
the Kaczmarz algorithm was shown to converge exponentially and independent of
number of equations. Recently an algorithm for finding sparse solution to a
linear system of equations has been proposed based on weighted randomized
Kaczmarz algorithm. These algorithms solves single measurement vector problem;
however there are applications were multiple-measurements are available. In
this work, the objective is to solve a multiple measurement vector problem with
common sparse support by modifying the randomized Kaczmarz algorithm. We have
also modeled the problem of face recognition from video as the multiple
measurement vector problem and solved using our proposed technique. We have
compared the proposed algorithm with state-of-art spectral projected gradient
algorithm for multiple measurement vectors on both real and synthetic datasets.
The Monte Carlo simulations confirms that our proposed algorithm have better
recovery and convergence rate than the MMV version of spectral projected
gradient algorithm under fairness constraints
Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery
In this work we address the problem of recovering sparse solutions to non
linear inverse problems. We look at two variants of the basic problem, the
synthesis prior problem when the solution is sparse and the analysis prior
problem where the solution is cosparse in some linear basis. For the first
problem, we propose non linear variants of the Orthogonal Matching Pursuit
(OMP) and CoSamp algorithms; for the second problem we propose a non linear
variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the
success rates of our algorithms on exponential and logarithmic functions. We
model speckle denoising as a non linear sparse recovery problem and apply our
technique to solve it. Results show that our method outperforms state of the
art methods in ultrasound speckle denoising
Matrix recovery using Split Bregman
In this paper we address the problem of recovering a matrix, with inherent
low rank structure, from its lower dimensional projections. This problem is
frequently encountered in wide range of areas including pattern recognition,
wireless sensor networks, control systems, recommender systems, image/video
reconstruction etc. Both in theory and practice, the most optimal way to solve
the low rank matrix recovery problem is via nuclear norm minimization. In this
paper, we propose a Split Bregman algorithm for nuclear norm minimization. The
use of Bregman technique improves the convergence speed of our algorithm and
gives a higher success rate. Also, the accuracy of reconstruction is much
better even for cases where small number of linear measurements are available.
Our claim is supported by empirical results obtained using our algorithm and
its comparison to other existing methods for matrix recovery. The algorithms
are compared on the basis of NMSE, execution time and success rate for varying
ranks and sampling ratios
Fast Acquisition for Quantitative MRI Maps: Sparse Recovery from Non-linear Measurements
This work addresses the problem of estimating proton density and T1 maps from
two partially sampled K-space scans such that the total acquisition time
remains approximately the same as a single scan. Existing multi parametric non
linear curve fitting techniques require a large number (8 or more) of echoes to
estimate the maps resulting in prolonged (clinically infeasible) acquisition
times. Our simulation results show that our method yields very accurate and
robust results from only two partially sampled scans (total scan time being the
same as a single echo MRI). We model PD and T1 maps to be sparse in some
transform domain. The PD map is recovered via standard Compressed Sensing based
recovery technique. Estimating the T1 map requires solving an analysis prior
sparse recovery problem from non linear measurements, since the relationship
between T1 values and intensity values or K space samples is not linear. For
the first time in this work, we propose an algorithm for analysis prior sparse
recovery for non linear measurements. We have compared our approach with the
only existing technique based on matrix factorization from non linear
measurements; our method yields considerably superior results
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