Comparison of Dictionary-Based Image Reconstruction Algorithms for Inverse Problems

Dogan, Didem
Öktem, Sevinç Figen
Many inverse problems in imaging involve measurements that are in the form of convolutions. Sparsity priors are widely exploited in their solutions for regularization as these problems are generally ill-posed. In this work, we develop image reconstruction methods for these inverse problems using patchbased and convolutional sparse models. The resulting regularized inverse problems are solved via the alternating direction method of multipliers (ADMM). The performance of the developed algorithms is investigated for an application in computational spectral imaging. Simulation results suggest that the convolutional sparse model provides similar reconstruction performance with the patch-based model; but the convolutional method is more advantageous in terms of computational cost.


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The usual goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface potentials and a mathematical model that relates the sources to the measurements. Due to attenuation and smoothing that occurs in the thorax, the inverse ECG problem is ill-posed and imposition of a priori constraints is needed to combat this ill-posedness. When the problem is posed in terms of reconstructing heart surface potentials, solutions have not yet achieved clinical utility; limitation...
Efficient algorithms for convolutional inverse problems in multidimensional imaging
Doğan, Didem; Öktem, Figen S.; Department of Electrical and Electronics Engineering (2020)
Computational imaging is the process of indirectly forming images from measurements using image reconstruction algorithms that solve inverse problems. In many inverse problems in multidimensional imaging such as spectral and depth imaging, the measurements are in the form of superimposed convolutions related to the unknown image. In this thesis, we first provide a general formulation for these problems named as convolutional inverse problems, and then develop fast and efficient image reconstruction algorith...
Bezek, Can Deniz; Öktem, Sevinç Figen; Department of Electrical and Electronics Engineering (2021-9-08)
Computational imaging is the process of forming images from indirect measurements using computation. In this thesis, we develop deep learning-based unrolled reconstruction methods for various computational imaging modalities. Firstly, we develop two deep learning-based reconstruction methods for diffractive multi-spectral imaging. The first approach is based on plug-and-play regularization with deep denoisers whereas the second one is an end-to-end learned reconstruction based on unrolling. Secondly, we con...
Comparison of Kalman filter and Bayesian-MAP approaches in the spatio-temporal solution of the inverse electrocardiography Ters elektrokardiyografinin zaman-uzamsal çözümünde Kalman filtre ve Bayes-MAP yöntemlerinin karşilaştirilmasi
Aydin, Ümit; Serinağaoğlu Doğrusöz, Yeşim (2010-07-15)
In this study some of the spatial and spatio-temporal methods for the solution of the inverse problem of electrocardiography (ECG) are compared with each other. Comparisons are also made for the cases with geometric errors, where the location of the heart is shifted for 10mm and the size of the heart is reduced by 5%. The compared methods are the Kalman filter and Bayesian maximum a posteriori estimation (MAP). Two different Bayesian-MAP algorithms are used. While one uses only spatial information the other...
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Altundag, H.; Taşeli, Hasan (2021-10-01)
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Citation Formats
D. Dogan and S. F. Öktem, “Comparison of Dictionary-Based Image Reconstruction Algorithms for Inverse Problems,” 28th Signal Processing and Communications Applications Conference (SIU) (2020), 2020, Accessed: 00, 2021. [Online]. Available: