An iterative hard thresholding algorithm for CS MRI

Abstract

The recently proposed compressed sensing theory equips us with methods to recover exactly or approximately, high resolution images from very few encoded measurements of the scene. The traditional ill-posed problem of MRI image recovery from heavily under-sampled -space data can be thus solved using CS theory. Differing from the soft thresholding methods that have been used earlier in the case of CS MRI, we suggest a simple iterative hard thresholding algorithm which efficiently recovers diagnostic quality MRI images from highly incomplete -space measurements. The new multi-scale redundant systems, curvelets and contourlets having high directionality and anisotropy, and thus best suited for curved-edge representation are used in this iterative hard thresholding framework for CS MRI reconstruction and their performance is compared. The -space under-sampling schemes such as the variable density sampling and the more conventional radial sampling are experimented at the same sampling rate and the effect of encoding scheme on iterative hard thresholding compressed sensing reconstruction is studied.

Magnetic resonance image reconstruction based on image decomposition constrained by total variation and tight frame

“…Equation () is the L 0 ‐norm non‐convex optimization problem, and the iterative hard thresholding algorithm (IHTA) has been demonstrated to be a highly effective solution method 22 . Besides, $$\Psi $$ in Equation () is a tight frame, and paper 12 has proposed a fast algorithm called pFISTA to solve the tight frame based L 1 norm problem.…”

“…Equation ( 8) is the L 0 -norm non-convex optimization problem, and the iterative hard thresholding algorithm (IHTA) has been demonstrated to be a highly effective solution method. 22 Besides, Ψ in Equation ( 8) is a tight frame, and paper 12 has proposed a fast algorithm called pFISTA to solve the tight frame based L 1 norm problem. Therefore, here we combine IHTA and pFISTA, denoted as projected fast iterative hard-thresholding algorithm (pFIHTA), to solve Equation ( 8):…”

GROG-pCS: GRAPPA Operator Gridding with CS-based p-thresholding for Under-sampled Radially Encoded MRI

“…𝝅 𝟐 × 𝑁 [15], where N is the readout point. This fully sampled radially encoded data was under-sampled retrospectively at various acceleration factors (4 ≤ AF ≤ 9) to test the viability of the proposed scheme.…”

“…There are some requirements for successful CS based MR image reconstruction: (i) data must be sparse (ii) image should contain incoherent artifacts (iii) the reconstruction technique should be non-linear. In the recent past, different algorithms have been applied for CS-based image reconstruction such as non-linear conjugate Gradient (NLCG), iterative hard thresholding Algorithm (IHTA), iterative soft thresholding algorithm (ISTA) [14,15] and iterative pthresholding algorithm [12]. Iterative thresholding methods [15] are a developing area of interest in CS signal recovery.…”

“…In the recent past, different algorithms have been applied for CS-based image reconstruction such as non-linear conjugate Gradient (NLCG), iterative hard thresholding Algorithm (IHTA), iterative soft thresholding algorithm (ISTA) [14,15] and iterative pthresholding algorithm [12]. Iterative thresholding methods [15] are a developing area of interest in CS signal recovery. This paper proposes an application of 'GROG followed by iterative p-thresholding based CS (GROG-pCS)' to reconstruct the MR images from the acquired non-Cartesian (radial) under-sampled k-space data.…”