Multi-dimensional Image Reconstruction using adaptive correlated noise model

Multi-dimensional Image Reconstruction using adaptive correlated noise model Venkatessh Ramakrishnan & Alessandro Foi Tampere University, Finland International VLBI Technology Workshop 2025 Motivation •Excerpt from Non-imaging data analysis in Synthesis Imaging in Radio Astronomy Volume II written by T. J. Pearson Spatially Adaptive UNiversal Algorithm (SAUNA) Signal acquisition Compression Compressed Sensing Sparsity-promoting nonlinear recovery Underlying Signal Measurements Reconstructed Signal Applications for Image & Signal Processing: Astronomy, Medicine, Radar, etc Signal acquisition Compression Compressed Sensing Sparsity-promoting nonlinear recovery Underlying Signal Measurements Reconstructed Signal Approach for nonlinear recovery: •Algorithm that packs an iterative sparse signal recovery framework •Models the residual degradation as spatial (and temporally) correlated noise Spatially Adaptive UNiversal Algorithm (SAUNA) Compressed Sensing (CS) •Technique for finding solution to undeterministic linear systems. •Image (JPEG) and movie (MPEG) formats are widely used with varying levels of compression either with or without loss of information •CS is the exact opposite of recovering a compressed and sparse signal to its original form Gridding –place for CS in radio interferometry •Transformation of 1-D complex visibilities into a 2-D image •Adopted approach involves the use of convolutional resampling to minimise aliasing artifacts and sidelobes •Size of the kernel is kept to about 7 uv cells to keep the computational cost low •CLEAN algorithm or those hybrid mapping iterating between deconvolution and self-calibration introduces additional complexity Requirements for CS in gridding •Sparsity is the first requirement for CS framework which is ubiquitous in radio interferometry •Artefacts due to aliasing and other reasons should be incoherent. This can be easily arrived by avoiding convolutional resampling. •The gridded image can then be denoised by retaining the sparsity Basics of noise: Additive White Gaussian Noise model Basics of noise: Coloured noise model Image reconstruction using AWGN & Correlated noise model Test for subarrays Summary & Future developments •Treatment of spatially correlated noise is fundamental in the precision cosmology era •Ironically, it is easier to model in the image plane than in visibilities •Joint spatial-temporal framework is nearing completion and will be available for the community by the end of 2025 •The current code is adaptable for both singleand multi-epoch imaging •Spectral-line correlated noise modelling along the lines of hyperspectral imaging is next in line •Followed by Polarisation where a nested noise model is tested since Q & U are complex