MRI Denoising using Sparse Based Curvelet Transform with Variance Stabilizing Transformation Framework

Abstract

We develop an efficient MRI denoising algorithm based on sparse representation and curvelet transform with variance stabilizing transformation framework. By using sparse representation, a MR image is decomposed into a sparsest coefficients matrix with more no of zeros. Curvelet transform is directional in nature and it preserves the important edge and texture details of MR images. In order to get sparsity and texture preservation, we post process the denoising result of sparse based method through curvelet transform. To use our proposed sparse based curvelet transform denoising method to remove rician noise in MR images, we use forward and inverse variance-stabilizing transformations. Experimental results reveal the efficacy of our approach to rician noise removal while well preserving the image details. Our proposed method shows improved performance over the existing denoising methods in terms of PSNR and SSIM for T1, T2 weighted MR images.

Compressed sensing with continuous parametric reconstruction

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Cooperative and feedback based authentic routing protocol for energy efficient IoT systems

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A Reweighted Symmetric Smoothed Function Approximating L0-Norm Regularized Sparse Reconstruction Method

“…where y y y ∈ R m is the compressed signal, and x x x ∈ R n is the k-sparse original signal (in most k nonzero elements, the rest of the n − k dimension is all zero), k is the sparsity of signal x x x, m n. Φ Φ Φ = [φ φ φ 1 , φ φ φ 2 , ..., φ φ φ n ] ∈ R m×n is a sensing matrix, where φ φ φ i ∈ R m , i = 1, 2, ..., n, which can be further represented as Φ Φ Φ = ψ ψ ψΩ Ω Ω, while ψ ψ ψ ∈ R m×n is a random matrix, and Ω Ω Ω ∈ R n×n is the sparse basis matrix [4,5] that a signal mapped to it can be sparse. b b b ∈ R m denotes measurement noise, which is only considered as an independent additive white Gaussian noise in this paper.…”