Advanced memory optimization techniques are reviewed to enhance the performance of Convolutional Neural Networks (CNNs) and Spiking Neural Networks (SNNs) on hardware accelerators, addressing the real-world challenges in medical imaging. This review evaluates various platforms: In-Memory Computing (IMC), Field-Programmable Gate Array (FPGA), Python Productivity for Zynq (PYNQ-Z2), Graphics Processing Unit (GPU), and Application-Specific Integrated Circuit (ASIC) concerning overcoming memory bottlenecks, minimizing latency, and reducing energy consumption in Magnetic Resonance Imaging (MRI) reconstruction, Computed Tomography (CT) scan analysis, and real-time diagnostics. It will analyze techniques like memory compression, tiling, hierarchical memory management, and neural network pruning to improve computation efficiency. In addition, in-memory computing will be a key focus to mitigate the inefficiency of data movement, adaptability of Field-Programmable Gate Array (FPGA) for custom workloads, parallel processing by Graphics Processing Unit (GPU), and domain-specific optimizations of Application-Specific Integrated Circuit (ASIC). This review addresses the challenges of high-resolution image processing and energy constraints to provide a comprehensive guide to scalable, efficient hardware accelerators for neural networks in medical imaging.