Optimising sampling theory for better image reconstruction
Real processes are continuous (analogue) yet computers are discrete (digital). Obtaining an accurate reconstruction of a signal is critically related to the sampling technique applied. The key is ensuring adequate representation without expending extra time and computational effort in collecting and analysing redundant data. Sampling theory is at the heart of signal processing with virtually limitless applications ranging from medical imaging to sound engineering to global positioning systems. EU-funded scientists initiated the project 'Generalized sampling and infinite-dimensional compressed sensing' (GESIDICS) to develop innovative sampling techniques that enhance reconstruction of the true signal from the model. The researchers dealt with the theory of generalised sampling that improves signal reconstruction by not imposing restrictions on the sampling or reconstruction space. While it is a powerful technique, it is known to fail in certain cases. GESIDICS scientists introduced a stable sampling rate to deliver a stable and convergent solution in cases of previous failure. This enabled the stable and accurate recovery of wavelet coefficients in a linear manner from Fourier samples in signals up to a certain constant value. These results clearly demonstrated that their algorithm is an optimal stable reconstruction scheme. GESIDICS has made a significant contribution to the mathematical field of sampling theory with important implications for enhanced signal processing. In particular, more accurate and consistent signal reconstruction from magnetic resonance images should have important impact on medical diagnostics and signal processing in general.
