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Reconstruction of Signal using Interpolation

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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...

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Image Reconstruction Using Analysis Model Prior.

Yu Han¹, Huiqian Du¹, Fan Lam²

¹School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.

Computational and Mathematical Methods in Medicine

|July 6, 2016

Summary

This summary is machine-generated.

This study introduces new priors into the analysis model for image reconstruction, improving performance. The novel method enhances image reconstruction from undersampled data, particularly for magnetic resonance imaging.

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Area of Science:

Signal Processing
Image Reconstruction
Applied Mathematics

Background:

The analysis model offers an alternative to sparse synthesis models for image reconstruction.
Cosparsity enables image reconstruction from undersampled data using analysis operators.
Existing methods lack sufficient prior information within the analysis framework.

Purpose of the Study:

To introduce and theoretically analyze additional prior information in the analysis model context.
To investigate uniqueness issues related to analysis operators, including general position and 2D finite difference operators.
To develop a novel image reconstruction model and algorithm with improved performance.

Main Methods:

Theoretical analysis of uniqueness issues for analysis operators.
Derivation of bounds on minimum measurement numbers.
Development of an iterative cosupport detection (ICD) based algorithm.
Testing on synthetic and magnetic resonance (MR) images.

Main Results:

Established theoretical bounds on minimum measurement numbers, outperforming existing methods.
Demonstrated significantly better reconstruction performance using the novel ICD-based model and algorithm.
Validated theoretical claims through simulations on diverse image datasets.

Conclusions:

Incorporating additional priors in the analysis model framework improves image reconstruction.
The proposed ICD-based method offers a robust and effective approach for reconstructing images from undersampled data.
The findings have implications for advanced imaging techniques, such as MR imaging.