Non linear sparse recovery algorithm

Das, Pallavi; Jain, Mansi; Majumdar, Angshul

doi:10.1109/isspit.2014.7300609

Cited by 6 publications

(12 citation statements)

References 9 publications

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“…Here we propose a simple algorithm to solve the problem by taking one step towards the solution of the non-linear least squares problem followed by a low-rank approximation via matrix factorization. In the past, similar strategies were used for solving non-linear sparse recovery problems [17][18][19]. Therein the task was to solve:…”

Section: Connection With Previous Workmentioning

confidence: 99%

Matrix factorization from non-linear projections: application in estimating T2 maps from few echoes

Khurana

Bhattacharjee

Majumdar

2015

Magnetic Resonance Imaging

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Section: Connection With Previous Workmentioning

confidence: 99%

Matrix factorization from non-linear projections: application in estimating T2 maps from few echoes

Khurana

Bhattacharjee

Majumdar

2015

Magnetic Resonance Imaging

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“…However, in essence they proposed an algorithm to recover a sparse solution to a linear problem where the cost function is not Euclidean. The only algorithmic work on solving nonlinear sparse recovery problems is [4]. There the authors proposed an l 1 -norm minimization approach; the recovery was posed as: min…”

Section: Literature Reviewmentioning

confidence: 99%

“…The algorithm in [4] is based on the Iterative Soft thresholding Algorithm. It is a two-step algorithm.…”

Section: Literature Reviewmentioning

confidence: 99%

“…For the linear case, it is easy to find the step size and the threshold τ ; but for nonlinear cases it is not. In [4], the step size was determined by the inverse of the Lipchitz bound of the cost function. But it is a very pessimistic (small) step size and the algorithm has very slow (linear) convergence rate.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In a previous study [4], a nonlinear l 1 -norm minimization problem was proposed to solve (5). The problem with such an approach is its slow convergence.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Greedy Algorithms for Non-linear Sparse Recovery

Gupta

Majumdar

2015

Machine Intelligence and Signal Processing

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In this work we propose two greedy algorithms to solve the underdetermined nonlinear sparse recovery problem. There are hardly any algorithms to solve such problems. Our algorithm is based on the OMP (Orthogonal Matching Pursuit) and the CoSaMP (Compressive Sampling Matching Pursuit), two popular techniques for solving the linear problem. We empirically test the success rates of our algorithms on exponential and logarithmic functions. The success rates follow a pattern similar to the one we observe for linear recovery problems.

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Fast Acquisition for Quantitative MRI Maps: Sparse Recovery from Non-Linear Measurements

Gogna

Majumdar

2016

2016 Data Compression Conference (DCC)

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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 multiparametric non-linear curve fitting techniques require a large number (8 or more) of echoes to estimate the mapsresulting 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 / 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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Non linear sparse recovery algorithm

Cited by 6 publications

References 9 publications

Matrix factorization from non-linear projections: application in estimating T2 maps from few echoes

Matrix factorization from non-linear projections: application in estimating T2 maps from few echoes

Greedy Algorithms for Non-linear Sparse Recovery

Fast Acquisition for Quantitative MRI Maps: Sparse Recovery from Non-Linear Measurements

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