Deconvolutionbased

Deconvolution-based methods are techniques to recover latent signals or images from blurred observations by reversing a convolution that models the imaging or sensing process. They assume the observed data arise from convolving a hidden signal with a blur kernel and then adding noise.

Model: y = k ⊗ x + n, where y is observed, x is latent signal, k is blur kernel, and n is noise. If k is known, deconvolution reduces to an inverse or regularized inversion.

Algorithms include Wiener filtering, Tikhonov regularization, and iterative methods such as Richardson–Lucy (for Poisson noise). Regularization stabilizes the solution by imposing prior constraints like smoothness or non-negativity. Blind deconvolution estimates both x and k from y, often with priors and iterative optimization.

Applications include image deblurring in photography and microscopy, astronomy, satellite imaging, spectroscopy, and seismic or acoustic signal restoration. In computational imaging, deconvolution-based approaches are combined with physical models to enhance resolution and contrast.

Key challenges are the ill-posedness of deconvolution, sensitivity to noise, dependence on an accurate blur kernel, nonuniform blur, and computational cost. Performance is evaluated with metrics such as PSNR or SSIM for images, or error norms for signals.

Related approaches include deconvolutional neural networks that learn deblurring operators from data and hybrid model-based/data-driven methods.