This dissertation studies AI-assisted medical image analysis in two applications: 1) breast cancer diagnosis on multiparametric magnetic resonance imaging (mpMRI) and 2) COVID-19 diagnosis and prognosis on chest radiography (CXR). MRI has become indispensable for breast imaging clinical practice and has evolved to mpMRI that include multiple sequences, including a T1-weighted dynamic contrast-enhanced (DCE) sequence, a T2-weighted (T2w) sequence, and a diffusion-weighted imaging (DWI) sequence. Computer-aided diagnosis (CADx) systems have been developed to help improve diagnostic performance and reduce reading time. The first aim of this dissertation investigates CADx methods, based on both human-engineered radiomic features and deep learning, that integrate complementary information provided by the various sequences in mpMRI in the task of distinguishing benign and malignant breast lesions, with the goal of leveraging the advancements in MRI technology to improve the breast lesion classification performance of current systems based on DCE-MRI alone. Three mpMRI fusion approaches, image fusion, feature fusion, and classifier fusion, are investigated. The findings suggest that leveraging the complementary information provided by various mpMRI sequences, especially using the feature fusion method, can improve the diagnostic performance of CADx in differentiating benign and malignant breast lesions. Although deep learning methods have demonstrated success in computer-aided medical imaging analysis, high dimensionality and data scarcity are unique challenges in medical imaging applications of deep learning. Transfer learning techniques with pretraining on two-dimensional images are often employed to circumvent the need for massive datasets, which have led to an underutilization of the high-dimensional, clinically valuable information in MRI. The second aim of this dissertation proposes and evaluates methods that incorporate the high-dimensional breast MRI without sacrificing computational efficiency or classification performance in distinguishing benign and malignant breast lesions. The feature maximum intensity projection method demonstrates the ability to effectively utilize volumetric information in MRI exams in two-dimensional CNN transfer learning, and the RGB channels effectively incorporate the fourth dimension in DCE and DWI. As COVID-19 emerged as a novel disease and developed into a pandemic, AI-assisted medical image analysis also holds promise to help optimize patient management and alleviate strains put on the healthcare system. The third aim of this dissertation investigates deep learning methods for the early diagnosis and accurate prognosis of COVID-19 using CXR images. A sequential transfer learning strategy follows a learning curriculum designed to pretrain and fine-tune a model on increasingly specific and complex tasks and eventually 1) distinguishes COVID-19 positive and negative patients using their initial CXR exam within two days of their initial RT-PCR test for COVID-19 and 2) predicts if a COVID-19 positive patient will potentially need intensive care in the next one to four days. Automatic lung segmentation and cropping are incorporated in the classification pipeline to reduce the influence of irrelevant image regions on model predictions. The role of soft tissue images is studied in addition to the standard CXR images. A weakly supervised learning technique, attention-based deep multiple instance learning, is also investigated for classifying and localizing COVID-19 involvement on CXR images. Promising performances are achieved in both tasks.