Nonconvex prior image constrained compressed sensing (NCPICCS): Theory and simulations on perfusion CT

Abstract

Purpose: To present and evaluate a new image reconstruction method for dynamic CT based on a nonconvex prior image constrained compressed sensing ͑NCPICCS͒ algorithm. The authors systematically compared the undersampling potential, functional information recovery, and solution convergence speed of four compressed sensing ͑CS͒ based image reconstruction methods using perfusion CT data: Standard ᐉ 1 -based CS, nonconvex CS ͑NCCS͒, and ᐉ 1 -based and nonconvex CS, including an additional constraint based on a prior image ͑PICCS and NCPICCS, respectively͒. Methods: The Shepp-Logan phantom was modified such that its uppermost ellipses changed attenuation through time, simulating both an arterial input function ͑AIF͒ and a homogeneous tissue perfusion region. Data were simulated with and without Poisson noise added to the projection data and subsequently reconstructed with all four CS-based methods at four levels of undersampling: 20, 12, 6, and 4 projections. Root mean squared ͑RMS͒ error of reconstructed images and recovered time attenuation curves ͑TACs͒ were assessed as well as convergence speed. The performance of both PICCS and NCPICCS methods were also evaluated using a kidney perfusion animal experiment data set. Results: All four CS-based methods were able to reconstruct the phantoms with 20 projections, with similar results on the RMS error of the recovered TACs. NCCS allowed accurate reconstructions with as few as 12 projections, PICCS with as few as six projections, and NCPICCS with as few as four projections. These results were consistent for noise-free and noisy data. NCPICCS required the fewest iterations to converge across all simulation conditions, followed by PICCS, NCCS, and then CS. On animal data, at the lowest level of undersampling tested ͑16 projections͒, the image quality of NCPICCS was better than PICCS with fewer streaking artifacts, while the TAC accuracy on the selected region of interest was comparable. Conclusions:The authors have presented a novel method for image reconstruction using highly undersampled dynamic CT data. The NCPICCS method takes advantage of the information provided by a prior image, as in PICCS, but employs a more general nonconvex sparsity measure ͓such as the ᐉ p -norm ͑0 Ͻ p Յ 1͔͒ rather than the conventional convex ᐉ 1 -norm. Despite the lack of guarantees of a globally optimal solution, the proposed nonconvex extension of PICCS consistently allowed for image reconstruction from fewer samples than the analogous ᐉ 1 -based PICCS method. Both nonconvex sparsity measures as well as prior image information ͑when available͒ significantly reduced the number of iterations required for convergence, potentially providing computational advantages for practical implementation of CS-based image reconstruction techniques.

Characterization of statistical prior image constrained compressed sensing (PICCS): II. Application to dose reduction

“…23,24,30,[34][35][36][37][38][39][40] In CT imaging, TV has favorable noise and artifacts mitigating properties but sometimes produce an image that lacks small and low-contrast details. 24 In contrast with many other applications of PICCS, [13][14][15][16][17][18][19][20][21][22][23][24] the primary goal of DR-PICCS is not to enable undersampled data acquisitions but rather to reduce image noise. 25,26 The enabling principle is an empirical property in PICCS: the noise level of an image reconstructed with PICCS is determined to some extent by the noise level of the prior image.…”

“…13) to reduce radiation dose in CT. PICCS was first proposed to enable view angle undersampling by integrating a prior image into the reconstruction procedure. [13][14][15][16][17][18][19][20][21][22][23][24] This framework can also be applied to the CT data acquisitions where the view angles are densely sampled but x-ray exposure levels are considerably reduced. For brevity, this type of PICCS applications has been referred to as dose reduction using PICCS (DR-PICCS).…”

Sequentially reweighted TV minimization for CT metal artifact reduction

“…23 Zou has proposed an iterative reweighted version of the LASSO algorithm. 24 In medical imaging, nonconvex approaches 25,26 that employ the l p -norm and weighted TV strategy 27 have been explored in breast tomosynthesis and computed tomography. In this work, the idea of reweighted l 1 -norm inspired the development of a systematic iterative approach for CT metal artifact reduction.…”

Radiation dose reduction in medical x‐ray CT via Fourier‐based iterative reconstruction

“…[5][6][7][8][9] According to the 2009 report from the National Council on Radiation Protection and Measurements, 10 CT accounts for about 15% of the total radiological examinations, but is disproportionately responsible for approximately 50% of the medical radiation exposure and nearly 25% of the total population exposure. Recently, the combination of real space iterative algorithms with modern optimization methods has been investigated for radiation dose reduction in CT. [11][12][13][14][15][16][17] Although these methods perform well under certain circumstances, currently the most popular method in clinical CT and other tomographic fields remains filtered back projection (FBP) and its variations. 18,19 In 2005, a Fourier-based iterative method, denoted Equally Sloped Tomography (EST), was developed to allow the 3D image reconstruction from a limited number of projections in parallel beam geometry.…”