Purpose To evaluate diagnostic image quality of 3D late gadolinium enhancement (LGE) with high isotropic spatial resolution (∼1.4 mm3) images reconstructed from randomly undersampled k‐space using LOw‐dimensional‐structure Self‐learning and Thresholding (LOST). Materials and Methods We prospectively enrolled 270 patients (181 men; 55 ± 14 years) referred for myocardial viability assessment. 3D LGE with isotropic spatial resolution of 1.4 ± 0.1 mm3 was acquired at 1.5T using a LOST acceleration rate of 3 to 5. In a subset of 121 patients, 3D LGE or phase‐sensitive LGE were acquired with parallel imaging with an acceleration rate of 2 for comparison. Two readers evaluated image quality using a scale of 1 (poor) to 4 (excellent) and assessed for scar presence. The McNemar test statistic was used to compare the proportion of detected scar between the two sequences. We assessed the association between image quality and characteristics (age, gender, torso dimension, weight, heart rate), using generalized linear models. Results Overall, LGE detection proportions for 3D LGE with LOST were similar between readers 1 and 2 (16.30% vs. 18.15%). For image quality, readers gave 85.9% and 80.0%, respectively, for images categorized as good or excellent. Overall proportion of scar presence was not statistically different from conventional 3D LGE (28% vs. 33% P = 0.17 for reader 1 and 26% vs. 31% P = 0.37 for reader 2). Increasing subject heart rate was associated with lower image quality (estimated slope = –0.009 (P = 0.001)). Conclusion High‐resolution 3D LGE with LOST yields good to excellent image quality in >80% of patients and identifies patients with LV scar at the same rate as conventional 3D LGE. Level of Evidence: 2 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2017;46:1829–1838.