Deconvolution with Least Squares

We are given a noisy observation x₀ = h ∗ x + noise. We want to recover the true sharp image x by solving the Tikhonov-regularized least-squares problem min_x ‖ h ∗ x − x₀ ‖₂² + λ ‖ x ‖₂². "Run" solves it using the either closed-form (exact) or gradient descent (iterative).

Method: Noise σ_n: 0.000 | Image:

Target

The sharp image x we want to recover.

Resize: 100%

Observation

x₀ = h ∗ x + noise

Blur σ: 0.5px

Deconvolved (Estimated)

x̂ ≈ argmin_x ‖ h ∗ x − x₀ ‖² + λ ‖ x ‖²

Regularization λ: 0.020

(click "Run")

Pixel-wise Difference

|x̂ − x| (Target vs. Deconvolved)

mean |xhat - x|: —