problems – Low-dose x-ray CT (Kang et al, Chen et al, Wolterink et al, Ye et al) – Sparse view CT (Jin et al, Han et al, Adler et al) – Interior tomography (Han et al) – Stationary CT for baggage inspection (Han et al) – CS-MRI (Hammernik et al, Schlemper et al, Yang et al, Lee et al, Zhu et al) – US imaging (Yoon et al ) – Diffuse optical tomography (Yoo et al) – Elastic tomography (Yoo et al) – Optical diffraction tomography (Kamilov et al) – etc • Advantages – Very fast reconstruction time – Significantly improved results Deep Learning for Inverse Problems
rectified linear unit (ReLU) ? • Why do we need a pooling and unpooling in some architectures ? • Why do some networks need fully connected layers whereas the others do not ? • What is the role of by-pass connection or residual network ? • What is the role of the filter channels in convolutional layer ? Many Mysteries…
matrix completion Nuclear norm Projection on sampling positions min m kH(m)k⇤ subject to P⌦(b) = P⌦(f) RankH(f) = k * Jin KH et al IEEE TCI, 2016 * Jin KH et al.,IEEE TIP, 2015 * Ye JC et al., IEEE TIT, 2016 m Annihilating filter-based low-rank Hankel matrix
Han, Y., & Ye, J. C. (2018). k-Space Deep Learning for Accelerated MRI. arXiv preprint arXiv:1805.03779. Proposed k-space Deep Learning ALOHA : k-space interpolation à k-space interpolation using deep learning ? Yes
Eung Yeop Kim and Jong Chul Ye 1 1 2 Dept. of Bio and Brain Engineering, KAIST, Dept. of Radiology, Gachon University Gil Mdeical Center 1 2 Motivation Ø To cover k-space data at different rate Ø Regular sampling pattern following view sharing of several temporal frames • Reconstruction using GRAPPA TWIST Fixed spatial resolution Limited temporal resolution How to reconstruct?
To improve temporal resolution of TWIST imaging using deep k-space learning Ø To generate multiple reconstruction results with various spatial and temporal resolution using one network VS = 5 VS = 2 CNN
gain • Has becomes mainstream topics • Deep convolutional framelets: • A new mathematical tool for understanding deep neural network for inverse problems • Biomedical image reconstruction • Key application for machine learning • Semi-supervised learning • New opportunities