Artificial intelligence (AI) is transforming medical imaging by improving diagnostic accuracy, streamlining workflows, and expanding access to specialist interpretation. These advances hold particular promise for low- and middle-income countries (LMICs) such as Ghana, where severe shortages of radiologists constrain timely diagnosis. Yet the introduction of AI also introduces substantial risks related to algorithmic bias, weak data governance, cybersecurity vulnerabilities, unclear clinical accountability, and dependence on external vendors. International guidance on trustworthy AI, while valuable, frequently presupposes institutional capabilities that many LMICs do not yet possess, creating a persistent policy-to-practice gap. This conceptual framework paper addresses that gap by proposing a seven-pillar governance framework for trustworthy AI in medical imaging, anchored in the Ghanaian context and designed for transferability across LMICs. The pillars comprise: (1) Governance and Leadership, (2) Ethical and Legal Compliance, (3) Data Governance and Security, (4) Clinical Validation and Safety, (5) Human Capacity Development, (6) Infrastructure and Digital Readiness, and (7) Monitoring, Auditing, and Continuous Improvement. The framework is operationalized through a five-level governance maturity model, measurable indicators, and a phased implementation roadmap. Drawing on international instruments (WHO, IMDRF, OECD, FUTURE-AI), comparative experiences from Rwanda, Kenya, Nigeria, South Africa, India, and other LMICs, and insights from institutional and technology governance theory, the paper translates high-level principles into practical institutional machinery. The contribution is both theoretical linking health policy, institutional, and technology governance perspectives and practical, offering decision-makers a capacity-proportionate pathway from aspirational policy to accountable practice.