Vol.:(0123456789) 1 3 International Journal of Computer Assisted Radiology and Surgery (2021) 16:1469–1480 https://doi.org/10.1007/s11548-021-02449-3 ORIGINAL ARTICLE Reducing reconstruction error of classifed textural patches by integration of random forests and coupled dictionary nonlinear regressors: with applications to super‑resolution of abdominal CT images Mahdieh Akbari 1  · Amir Hossein Foruzan 1  · Yen‑Wei Chen 2  · Hongjie Hu 3 Received: 7 December 2020 / Accepted: 30 June 2021 / Published online: 14 July 2021 © CARS 2021 Abstract Purpose Random forests and dictionary-based statistical regressions have common characteristics, including non-linear mapping and supervised learning. To reduce the reconstruction error of high-resolution images, we integrate random forests and coupled dictionary learning. Methods Textural diferences of image blocks are considered by the classifcation of patches using an Auto-Encoder network. The proposed algorithm partitions an input LR image by 5 × 5 blocks and classifes training patches into six categories. A single random forest regressor is then trained corresponding to each class. The output of an RF is considered as an initial estimate of the HR slice. If a slice’s representation is sparse in the Discrete Cosine Transform domain, the initial reconstructed image is further improved by a coupled dictionary. Results In this study, we applied our method to abdominal CT scans and compared them to conventional and recent researches. We achieved an average improvement of 0.06 (2.37) using the SSIM (PSNR) index compared to the random forest + dictionary learning method. Conclusion The low standard deviation of the results reveals the stability of the proposed method as well. The proposed algorithm depicts the efectiveness of classifying image patches and individual treatment of each class. Keywords Super-resolution · Random forests · Coupled dictionary learning · Auto-encoders · Abdominal CT images Introduction Super‑resolution of medical images Providing high-resolution medical images by software or hardware techniques facilitates the diagnosis of diseases. Software approaches are an alternative to hardware meth- ods, and they can reduce radiation dose, acquisition time, and costs of imaging devices. There are challenges in super- resolution (SR) methods, such as obtaining high-frequency details and preventing visual artifacts [1–3]. SR image reconstruction approaches are divided into interpolation, model-based, and machine learning catego- ries. Interpolation techniques employ a fxed mathematical model, and they estimate the gray level of missing pixels using the intensities of nearby points. Model-based methods represent the degradation of a low-resolution (LR) image by a mathematical equation that consists of warping, blurring, * Amir Hossein Foruzan a.foruzan@shahed.ac.ir; aforuzan@yahoo.com Mahdieh Akbari mahdyeh.akbari@shahed.ac.ir Yen-Wei Chen chen@is.ritsumei.ac.jp Hongjie Hu hongjiehu@zju.edu.cn 1 Department of Biomedical Engineering, Shahed University, Persian Gulf Highway, 33191-18651 Tehran, Iran 2 Intelligent Image Processing Lab, College of Information Science and Engineering, Ritsumeikan University, Shiga, Japan 3 Department of Radiology, Sir Run Run Shaw Hospital, Zhejiang University, Hangzhou, Zhejiang, China