deconvoluie

Deconvoluie refers to the process of reversing the effects of convolution in order to recover an original signal or source distribution from data that has been convolved with a known or estimated kernel. It is used in signal processing and imaging to counter blur from the system's impulse response, such as optical blur, instrumental response, or seismic spreading.

Model: observed data g = f * h + n, with f the original signal, h the point spread function or kernel. Deconvoluie aims to estimate f given g and h, or to estimate h when it is uncertain. The problem is often ill-posed and requires regularization or probabilistic priors.

Common methods include Wiener deconvolution (frequency-domain with noise considerations), the Richardson-Lucy algorithm (iterative maximum-likelihood for Poisson noise), and blind deconvolution (estimating f and h together). Regularization techniques such as Tikhonov or sparsity priors, and Bayesian approaches, help stabilize solutions.

Applications span astronomical imaging, microscopy, photography, medical imaging, and geophysics. Deconvolution improves resolution and contrast, aids feature localization, and supports quantitative measurements when the kernel is known or well-estimated.

History and development: early inverse problems led to deconvolution methods in signal processing, with notable algorithms such as Lucy–Richardson developed in the 1970s. Modern approaches combine Bayesian inference, machine learning priors, and blind strategies to handle imperfect kernels and noisy data.

See also: deconvolution, inverse problem, point spread function, regularization, Wiener filter, Richardson–Lucy deconvolution, blind deconvolution.