We define its regularized counterpart R ∗ as (5) R ∗ = 1 − λ R ~ + λ I s + 1, λ ∈ 0,1, where I s +1 denotes a unit matrix of size (s + 1)×(s + 1).
Specifically, for an input matrix M of size s by l, we create a matrix M′ of size s by 2 l.
The following parameters were used: detector collimation 128 × 0.625 mm; pitch 1.0; rotation time 0.5 s; matrix size 512 × 512.
For direct comparison, one subject (female, 25 years) of the 7 T study population underwent 3 T scanning with the identical paradigm used at 7 T (TR = 1.8 s; matrix size: 128 px × 128 px × 23 slices).
For comparison, 15 healthy volunteers (different from the 7 T group; 7 females, 8 females, mean age ± SD: 25.4 ± 3.4 years) participating in an ongoing study on a high field whole body 3 T MRI scanner (Siemens Trio, Siemens Medical, Erlangen, Germany), performed an emotion discrimination task comparable to the design and setup described above (TR = 1.8 s; matrix size: 128 px × 128 px × 20 slices).
For planar imaging, anterior and posterior images of the lung and liver were acquired over 120 s each and matrix size 256 × 256.
SPECT of the head and neck region was acquired by the step-and-shoot mode, one step per 3°, 30 s per frame, matrix size 128 × 128, using a dual-head gamma camera (Genesis, Philips, Best, The Netherlands) equipped with low-energy, high-resolution collimators.
Slice-selective IR-FSE (ssIR-FSE) and non-slice-selective IR-FSE (nsIR-FSE) images were collected using a TR of 3 s, a TE of 20 ms, and an effective TE of 50 ms with an echo train length of 4, a slice thickness of 2 mm, an FOV of 4 cm, an inversion time (TI) of 1.5 s, and a matrix size of 256 × 128.
Functional images were acquired using a Q2TIPS pulse arterial spin labeling sequence (Luh et al. 1999) with the following parameters: field of view = 192 mm × 192 mm, matrix size = 64 × 64, TR = 2 s, TE = 17 ms, TI1 = 700 ms, TI2 = 1400 ms, T1s = 1050 ms, flip angle = 72°, slice thickness = 7 mm, slice gap = 3 mm.
Then, for each matrix R l s, a linear form of size S has to be estimated.
