Image reconstruction under multiplicative speckle noise using total variation

Abstract

a b s t r a c tIn this paper, we present a method for reconstructing images or volumes from a partial set of observations, under the Rayleigh distributed multiplicative noise model, which is the appropriate algebraic model in ultrasound (US) imaging. The proposed method performs a variable splitting to introduce an auxiliary variable to serve as the argument of the total variation (TV) regularizer term. Applying the Augmented Lagrangian framework and using an iterative alternating minimization method lead to simpler problems involving TV minimization with a least squares term. The resulting Gauss Seidel scheme is an instance of the Alternating Direction Method of Multipliers (ADMM) method for which convergence is guaranteed. Experimental results show that the proposed method achieves a lower reconstruction error than existing methods.

GPR Target Detection by Joint Sparse and Low-Rank Matrix Decomposition

“…In particular, ALM has received considerable attention due to its simple form and decoupling of variables. It has been used in compressed sensing [38], [39], image restoration and reconstruction [40], [41], and matrix completion and recovery [34], [42]. ALM is often used to solve convex, non-smooth objective functions with linear constraints.…”

“…26and (27) for JLRS-SP require a matrix inversion, which has a computational complexity of O((JN ) 3 ). For JLRS-AP, the solutions of (40) and (41) cost O((M N ) 3 ) operations. The computational cost can be reduced to O(J 3 + N 3 ) for JLRS-SP and O(M 3 + N 3 ) for JLRS-SP when applying the Bartels-Stewart algorithm.…”

SAR image despeckling using plug‐and‐play ADMM

“…The drawback of using regularisers is that it requires prior information about the image. Rayleigh distributed speckle noise removal for ultrasound images using TV regularisation has been addressed and solved using ADMM in [18]. Figueiredo and Bioucas‐Dias [19] proposed Poisson image deconvolution by AL (PIDAL) and solved it using ADMM with the help of a TV regulariser.…”

Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage

“…For example, in [ 13 ], undersampled fMRI data are reconstructed using CS with sparsity of fMRI data in the wavelet domain, wherein orthogonal Daubechies wavelet is used as the sparsifying basis. This is to note that CS-based sparse recovery methods are being used extensively in many applications including other medical imaging modalities [ 19 , 20 ] and in videos [ 21 , 22 ].…”