Notes : Noise and Image Reconstruction with Noise ( lecture 11 )

where b ∈ RM is a vectorized representation of M measurements, x ∈ RN is the vector of N unknowns, and A ∈ RM×N is the system matrix. In many imaging problems, the measurements are corrupted by noise. Although there are a variety of different sources, such as quantization, saturation, thermal, analog to digital conversion, and compression, typical image reconstruction problems deal with one of two models: signal-independent i.i.d. Gaussian noise or signal-dependent Shot or Poisson noise. A combination of both additive Gaussian and signal-dependent Poisson noise is also common.