The eight coil sensitivity magnitude maps used in simulations that were estimated from the data acquired on MR scanner.

<p>The eight coil sensitivity magnitude maps used in simulations that were estimated from the data acquired on MR scanner.</p

MCS-MRI reconstruction on <i>in vivo</i> brain images using acquired noiselet encoded and Fourier encoded data for different acceleration factors (up/down: phase encodes, left/right: frequency encode).

<p><b>(a)</b>: shows reference image reconstructed from fully sampled Fourier encoded data; <b>(b)-(d)</b>: show images reconstructed using Fourier encoding for acceleration factor of 2.6, 4 and 8 respectively; <b>(e)-(g)</b>: show the difference images using Fourier encoding for acceleration factor of 2.6, 4 and 8 respectively; <b>(h)</b>: shows reference image reconstructed from fully sampled Noiselet encoded data; <b>(i)-(k)</b>: show images reconstructed using noiselet encoding for acceleration factor of 2.6, 4 and 8 respectively; <b>(l)-(n)</b>: show the difference images using noiselet encoding for acceleration factor of 2.6, 4 and 8 respectively. It can be seen from the difference images that noiselet encoding outperforms Fourier encoding on the acquired invivo data. The loss in resolution is clearly visible for Fourier encoding at an acceleration factor of 8.</p

MCS-MRI reconstruction on the acquired noiselet encoded and Fourier encoded data for different acceleration factors (up/down: phase encodes, left/right: frequency encode).

<p><b>RF</b>: shows reference image reconstructed from fully sampled Fourier encoded data; <b>RN</b>: shows reference image reconstructed from fully sampled Noiselet encoded data; <b>(a)-(c)</b>: show images reconstructed using Fourier encoding for acceleration factor of 4, 8 and 16 respectively; <b>(d)-(f)</b>: show the difference images using Fourier encoding for acceleration factor of 4, 8 and 16 respectively; <b>(g)-(i)</b>: show images reconstructed using noiselet encoding for acceleration factor of 4, 8 and 16 respectively; <b>(j)-(l)</b>: show the difference images using noiselet encoding for acceleration factor of 4, 8 and 16 respectively. The result here aligns with the simulation results and noiselet encoding outperforms Fourier encoding in preserving resolution. <b>(A-H)</b>: Zoomed portion of phantom images reconstructed with Fourier encoding and noiselet encoding with different acceleration factors. <b>(A)</b>: shows the original image reconstructed from fully sampled Fourier encoded data; <b>(B), (C) and (D)</b>: show the Fourier encoded reconstructed images for acceleration factors of 4, 8 and 16 respectively; <b>(E)</b>: shows the image reconstructed from fully sampled noiselet encoded data; <b>(F), (G) and (H)</b>: show the noiselet encoded reconstructed images for acceleration factors of 4, 8 and 16 respectively demonstrating that noiselet encoding produces improved resolution images than than Fourier encoding at all acceleration factors.</p

Simulation results for MCS-MRI comparing the noiselet encoding and Fourier encoding schemes (up/down: phase encodes, left/right: frequency encode) using only wavelet penalty.

<p><b>(a)-(b)</b>: show images reconstructed with Fourier encoding for acceleration factors of 4 and 8 respectively; <b>(c)-(d)</b>: show difference images with Fourier encoding for acceleration factors of 4 and 8 respectively; <b>(e)-(f)</b>: show images reconstructed with noiselet encoding for acceleration factors of 4 and 8 respectively; <b>(g)-(h)</b>: show difference images with noiselet encoding for acceleration factors of 4 and 8 respectively.</p

The mean relative error and standard deviation (vertical bar) versus the number of receive channels for acceleration factors of 2 and 3, showing that the error increases as the number of channels decreases.

<p>Noiselet encoding outperforms Fourier encoding for both acceleration factors when the number of channels is more than two. However for a single channel, noiselet encoding outperforms Fourier encoding only for the acceleration factor of 2.</p

Simulation results for MCS-MRI comparing the noiselet encoding and Fourier encoding schemes (up/down: phase encodes, left/right: frequency encode).

<p><b>(a)-(c)</b>: show images reconstructed with Fourier encoding for acceleration factors of 4, 8, and 16 respectively; <b>(d)-(f)</b>: show difference images with Fourier encoding for acceleration factors of 4, 8, and 16 respectively; <b>(g)-(i)</b>: show images reconstructed with noiselet encoding for acceleration factors of 4, 8, and 16 respectively; <b>(j)-(l)</b>: show difference images with noiselet encoding for acceleration factors of 4, 8, and 16 respectively; <b>(m)-(n)</b>: show zoomed portion of images reconstructed with Fourier encoding for acceleration factors of 8, and 16 respectively; <b>(o)-(p)</b>: show zoomed portion of images reconstructed with noiselet encoding for acceleration factors of 8, and 16 respectively. The zoomed images highlight that MCS-MRI using noiselet encoding reconstructions outperforms the Fourier encoding for preserving image resolution.</p

Images reconstructed using fully sampled noiselet encoded and Fourier encoded data acquired on the 3T scanner (up/down: phase encodes, left/right: frequency encode).

<p>The noiselet encoded data was acquired using the pulse sequence described in section III C, and Fourier encoded data was acquired using a conventional spin echo sequence. <b>(c)-(f)</b>: show the zoomed portion of the images in (b) and (e) respectively, with the zoomed images demonstrating that noiselet encoding provides similar image resolution to that of Fourier encoding; <b>(g)-(h)</b>: show T2 and T1 weighted brain images using noiselet encoding respectively; <b>(i)-(j)</b>: show T2 and T1 weighted brain images using Fourier encoding respectively. These <i>in vivo</i> images demonstrate the practical feasibility of the proposed noiselet encoding scheme.</p

The mean relative error and standard deviation (vertical bar) versus the acceleration factor in MCS-MRI highlighting that noiselet encoding consistently outperforms Fourier encoding.

<p>The mean relative error and standard deviation (vertical bar) versus the acceleration factor in MCS-MRI highlighting that noiselet encoding consistently outperforms Fourier encoding.</p

MAEs of KEM reconstructed images from noisy and denoised sinogram datasets.

MAEs of KEM reconstructed images from noisy and denoised sinogram datasets.</p

S1 Data -

(XLSX)</p