Compressively Sampled MR Image Reconstruction Using Hyperbolic Tangent-Based Soft-Thresholding

Abstract

The application of compressed sensing (CS) to magnetic resonance (MR) images utilizes the transformed domain sparsity to enable the reconstruction from an under-sampled k-space (Fourier) data using a non-linear recovery algorithm. In order to estimate the missing k-space data from the partial Fourier samples, the reconstruction algorithms minimize an objective function based on mixed l 1 -l 2 norms. Iterative-shrinkage algorithms, such as parallel coordinate descent (PCD) and separable surrogate functional, provide an efficient numerical technique to minimize the l 1 -regularized least square optimization problem. These algorithms require a thresholding step to induce sparsity in the solution, which is an essential requirement of the CS recovery. This paper introduces a novel soft-thresholding method based on the hyperbolic tangent function. It has been shown that by using the proposed thresholding function in the sparsifying domain and a data consistency step in the k-space, the iterative-shrinkage algorithms can be used effectively to recover the under-sampled MR images. For the purpose of demonstration, we use the proposed soft-thresholding and data consistency with the PCD algorithm and compare its performance with the conventional PCD, projection onto convex sets and low-resolution reconstruction methods. The metrics used to compare the various algorithms are the artifact power, the peak signal-to-noise ratio, the correlation and the structural similarity index. The experimental results are validated using SheppLogan phantom image as well as real human head MR images taken from the MRI scanner at

De-Noising of Sparse Signals Using Mixture Model Shrinkage Function

“…In our de-noising/reconstruction of the sparse signals and images, we addressed this problem. Some of the methods used for de-noising and recovery of sparse signals are soft thresholding [1], hard thresholding [2], firm thresholding [5], and hyperbolic tangent thresholding [7]. An improved total variation regularization is applied to remove salt and pepper noise from images [36].…”

“…Different sparsity-based algorithms have been developed in the past to de-noise and recover sparse signals and images, that is, soft thresholding [1], hard thresholding [2], [3], [4], firm thresholding [5], non-negative garrote thresholding [6], hyperbolic tangent thresholding [7], logarithmic thresholding [8], hankel sparse low-rank approximation [9], proximal operators [10], [11], [12], alternating direction method of multipliers [13], [14], block thresholding [15], and overlapping group shrinkage (OGS) [16]. Along with these established techniques, some new techniques are also used for de-noising of specific image types.…”

“…Along with these established techniques, some new techniques are also used for de-noising of specific image types. Jawad in [7] uses hyperbolic tangent thresholding and Hayat in [8] uses logarithmic based thresholding for de-noising biomedical images. An adaptive thresholding method based on neural networks is used for de-noising of Gaussian and speckle noise in natural,…”

Efficient Reconstruction Technique for Multi-Slice CS-MRI Using Novel Interpolation and 2D Sampling Scheme

“…With the edge of this reduced scan time, CS-MRI has additional computational overhead compared to standard MRI where only inverse Fourier transform is enough [22]. The CS-MRI trends can be broadly categorized as methods focused on improving the reconstruction strategies [23,24], and parallel CS-MRI techniques [25]. For successful CS-MRI, the sparse regularization can be achieved in a specific transform domain or using some dictionary learning techniques [26][27][28][29][30][31].…”

Radial Undersampling-Based Interpolation Scheme for Multislice CSMRI Reconstruction Techniques

“…The recent trends of CSMRI can be classified as techniques dedicated to improved reconstruction techniques [43][44][45] and parallel CSMRI approaches [4,5,40,42,46,47]. In CSMRI, the sparse regularization has been accomplished BioMed Research International through a particular transform domain, such as the wavelet [10] and curvelet [48], or through some dictionary learning approaches [49][50][51][52][53][54][55].…”