  The large volume and complexity of medical imaging datasets are bottlenecks
for storage, transmission, and processing. To tackle these challenges, the
application of low-rank matrix approximation (LRMA) and its derivative, local
LRMA (LLRMA) has demonstrated potential. A detailed analysis of the literature
identifies LRMA and LLRMA methods applied to various imaging modalities, and
the challenges and limitations associated with existing LRMA and LLRMA methods
are addressed. We note a significant shift towards a preference for LLRMA in
the medical imaging field since 2015, demonstrating its potential and
effectiveness in capturing complex structures in medical data compared to LRMA.
Acknowledging the limitations of shallow similarity methods used with LLRMA, we
suggest advanced semantic image segmentation for similarity measure, explaining
in detail how it can be used to measure similar patches and its feasibility. We
note that LRMA and LLRMA are mainly applied to unstructured medical data, and
we propose extending their application to different medical data types,
including structured and semi-structured. This paper also discusses how LRMA
and LLRMA can be applied to regular data with missing entries and the impact of
inaccuracies in predicting missing values and their effects. We discuss the
impact of patch size and propose the use of random search (RS) to determine the
optimal patch size. To enhance feasibility, a hybrid approach using Bayesian
optimization and RS is proposed, which could improve the application of LRMA
and LLRMA in medical imaging.
