Compressed Sensing Image Reconstruction Via Recursive Spatially Adaptive Filtering

We introduce a new approach to image reconstruction from highly incomplete data. The available data are assumed to be a small collection of spectral coef?cients of an arbitrary linear transform. This reconstruction problem is the subject of intensive study in the recent ?eld of "compressed sensing" (also known as "compressive sampling"). Our approach is based on a quite speci?c recursive ?ltering procedure. At every iteration the algorithm is excited by injection of random noise in the unobserved portion of the spectrum and a spatially adaptive image denoising ?lter, working in the image domain, is exploited to attenuate the noise and reveal new features and details out of the incomplete and degraded observations. This recursive algorithm can be interpreted as a special type of the Robbins-Monro stochastic approximation procedure with regularization enabled by a spatially adaptive ?lter. Overall, we replace the conventional parametric modeling used in CS by a nonpa...

• Type: Conference
• Year: 2007
• Where: ICIP
• Authors: Karen O. Egiazarian, Alessandro Foi, Vladimir Katkovnik
• Keywords: Exact Reconstruction, ICIP 2007, Image Processing, Image Reconstruction, Recursive Algorithm, Recursive Filtering Procedure, Stochastic Approximation Procedure