Probabilistic Graphical Model for Image Reconstruction
Image reconstruction algorithm based on a probabilistic graphical model by Shanrui Zhang explores filling missing pixels in images. It utilizes compressed sensing to achieve the effect of full sampling, mapping signal dimensions, and estimating signals using a hierarchical prior model.
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Presentation Transcript
Image Reconstruction Algorithm Based on Probabilistic Graphical Model Shanrui Zhang csc696
1.Problem 2.Approach 3.Results
Image Reconstruction Image reconstruction Image reconstruction is a technology that fills in the missing pixels in the image and reconstructs based on the pixel information of the background. Compressed sensing In the process of signal sampling, a few sampling points are used to achieve the same effect as full sampling.
The observation matrix maps the high-demensional signal X to the low-demension space y:observation value (known,compressed image)(demension M) :observation matrix (sparse sampling) :sparse matrix (Fourier transform)(signal->frequency) s:sparse index (natural singal x not sparse) x:input signal (unknow,we need to recover) (demension N)
In general, the overall goal of signal representation is to estimate a vector from a mathematical model of Among them, is the observation vector, is the additive Gaussian random white noise, its variance matrix is , and is the noise precision coefficient. Matrix is a dictionary matrix with columns greater than rows ( ). is the vector to be estimated. C = + y M y C M C M L C I 0 1 L = + y Factorize the joint probability density function of and express it with a 3-L hierarchical prior model as follows: The factor graph of the 3-L model can be obtained from the factorization of the 3-L hierarchical prior model. The vector graphical model of the 3-L hierarchical model. f f fy f f
Algorithm 1. Initialize , , 2. Compute the mean and variance of during the first iteration: = y ( = + H ) -1 H -1 3. Update , , , during subsequent iterations. M = y 2 2 + 1 a + = l l b l l ( ) ( ) 2 2 + + + 2 2 4 l ll l = l 2 l 4. After several iterations, the estimated value of is obtained after the algorithm converges: = f f fy f f
