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Transcript of Final Review
Sparse Image Reconstruction
with Application to MRFM -R.Vishnoo Verdhen
Objective The main objective of the project is to reconstruct
sparse images when the observations are obtained
from linear transformations and corrupted by an
additive white Gaussian noise.
Existing System There is no previous algorithm which is used for the quality reconstruction of the sparse image.
Proposed System We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero.
To overcome the complexity of the posterior distribution, a Gibbs sampling algorithm is proposed.
The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution.
The algorithm provides more information and also also in quality reconstruction than the proposed sparse reconstruction methods that only give a point estimate.
Modules User Interface
Reconstruction User Interface Need to interact
Show the input,process and display output
Designed using Swing Package in Java
Designed in such a way that it is apparent and recognizable to users. Get Image Gets the image to be used for reconstruction
Opens only standard image formats like jpeg,bmp,etc
Basic step in the project
Scaling Process of measuring or ordering entities with respect to quantitative attributes or traits.
Single pixel size is extended to a larger extend.
The posterior of the image is stretched to either a 3 X 3 or a maximum of 9 X 9
Reconstruction Gibbs Sampling Algorithm is used in the process
A single pixel is broken into many pixels and is reconstructed again with the algorithm to get a clear picture without much Gaussian noise.
First the image is generated such that it has non zero values in each slice.
The image to be recovered is convolved and as a result a clearer picture is got than it was before.
Gibbs Sampling Algorithm Used to generate a sequence of samples from the joint probability distribution of two or more random variables.
Purpose is to approximate the Joint Distribution
Initializes the values for the nonzero pixels intensities.
It is then iterated till a clear sample can be obtained.
Thus the algorithm generates samples according to the posterior distribution.
Demo Sparsed Image
Scaled Image Reconstructed Image An efficient Gibbs sampler was used to generate samples according to this posterior distribution.
The unknown hyperparameters of the model were integrated out from the posterior distribution of the image producing a full posterior distribution that can be used for estimation of the pixel values by maximization
Conclusion Future Scope Future work will include extension of the proposed method to other sparse bases, inclusion of uncertain point spread functions, and investigation of molecular priors.
Scope It is used to solve a general denoising problem in a non-Bayesian quasi-maximum likelihood estimation framework.
Also for sparse reconstruction of noisy images, including MRFM.