Journal ArticleDOI
Learning Sparsifying Transforms
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TLDR
This work proposes novel problem formulations for learning sparsifying transforms from data and proposes alternating minimization algorithms that give rise to well-conditioned square transforms that show the superiority of this approach over analytical sparsify transforms such as the DCT for signal and image representation.Abstract:
The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular especially in applications such as image denoising, inpainting, and medical image reconstruction. While there has been extensive research on learning synthesis dictionaries and some recent work on learning analysis dictionaries, the idea of learning sparsifying transforms has received no attention. In this work, we propose novel problem formulations for learning sparsifying transforms from data. The proposed alternating minimization algorithms give rise to well-conditioned square transforms. We show the superiority of our approach over analytical sparsifying transforms such as the DCT for signal and image representation. We also show promising performance in signal denoising using the learnt sparsifying transforms. The proposed approach is much faster than previous approaches involving learnt synthesis, or analysis dictionaries.read more
Citations
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Journal ArticleDOI
Image Reconstruction is a New Frontier of Machine Learning
TL;DR: This special issue focuses on data-driven tomographic reconstruction and covers the whole workflow of medical imaging: from tomographic raw data/features to reconstructed images and then extracted diagnostic features/readings.
Journal ArticleDOI
LEARN: Learned Experts’ Assessment-Based Reconstruction Network for Sparse-Data CT
Hu Chen,Yi Zhang,Yunjin Chen,Junfeng Zhang,Weihua Zhang,Huaiqiang Sun,Yang Lv,Peixi Liao,Jiliu Zhou,Ge Wang +9 more
TL;DR: In this paper, a learned experts' assessment-based reconstruction network (LEARN) was proposed for sparse-data computed tomography (CT) reconstruction, which utilizes application-oriented knowledge more effectively and recovers underlying images more favorably than competing algorithms.
Journal ArticleDOI
Structured Overcomplete Sparsifying Transform Learning with Convergence Guarantees and Applications
TL;DR: The promising performance of the proposed approach in image denoising is shown, which compares quite favorably with approaches involving a single learned square transform or an overcomplete synthesis dictionary, or gaussian mixture models.
Journal ArticleDOI
Image Reconstruction: From Sparsity to Data-Adaptive Methods and Machine Learning
TL;DR: The field of medical image reconstruction has seen roughly four types of methods: analytical methods, such as filtered backprojection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems.
Journal ArticleDOI
Learning-Based Compressive MRI
Baran Gozcu,Rabeeh Karimi Mahabadi,Yen-Huan Li,Efe Ilicak,Tolga Çukur,Jonathan Scarlett,Volkan Cevher +6 more
TL;DR: In this article, a learning-based framework for optimizing MRI subsampling patterns for a specific reconstruction rule and anatomy, considering both the noiseless and noisy settings, is proposed.
References
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