# Mask iterative hard thresholding algorithms for sparse image reconstruction of objects with known contour

@article{Dogandzic2011MaskIH, title={Mask iterative hard thresholding algorithms for sparse image reconstruction of objects with known contour}, author={Aleksandar Dogandzic and Renliang Gu and Kun Qiu}, journal={2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)}, year={2011}, pages={2111-2116} }

We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct is known and that the signal outside the contour is zero, we formulate a constrained residual squared error minimization problem that incorporates both the geometric information (i…

## 17 Citations

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## References

SHOWING 1-10 OF 13 REFERENCES

Algorithms for sparse X-ray CT image reconstruction of objects with known contour

- Computer Science
- 2012

A constrained residual squared error minimization criterion is proposed that incorporates both the knowledge of the object's contour and signal sparsity in an appropriate transform domain and convex relaxation and greedy approaches to approximately solving this minimization problem are presented.

Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

- Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2007

This paper proposes gradient projection algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems and test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method.

A Fast Algorithm for Sparse Reconstruction Based on Shrinkage, Subspace Optimization, and Continuation

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2010

The code FPC_AS embeds this basic two-stage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence of values to $\mu$ and exhibits state-of-the-art performance in terms of both its speed and its ability to recover sparse signals.

Compressive sensing of images with a priori known spatial support

- MathematicsMedical Imaging
- 2010

In this work, incorporation of either complete or partial a priori knowledge of object spatial support into the compressive sensing (CS) framework is investigated and the proposed augmented reconstruction model was shown to be robust to inaccuracies in the estimated object support.

Computational Methods for Sparse Solution of Linear Inverse Problems

- Computer ScienceProceedings of the IEEE
- 2010

This paper surveys the major practical algorithms for sparse approximation with specific attention to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available.

Principles of Computerized Tomographic Imaging

- Physics
- 2000

The total attenuation suffered by one beam of x-rays as it travels in a straight line through an object can be represented by a line integral. Combining a set of line integrals forms a projection.…

Matrix Algebra From a Statistician's Perspective

- Mathematics
- 1998

Preface. - Matrices. - Submatrices and partitioned matricies. - Linear dependence and independence. - Linear spaces: row and column spaces. - Trace of a (square) matrix. - Geometrical considerations.…

A fast algorith m for sparse reconstruction based on shrinkage, subspace optimi zation, and continuation,”SIAM

- J. Sci. Comput. , vol. 32,
- 2010

Computational methods for s parse solution of linear inverse problems

- Proc. IEEE, vol. 98, no. 6, pp. 948–958, 2010.
- 2010