x and ∇ ( i ) > δ ϵ m a x \nabla ^>\delta \epsilon _ repeat the following: solve for s t ( i ) → s t ( i ) = s − e θ ( i ) ( f ) x f = e θ ( i ) ( t ) x t ^\,\to s_^\,=\,s\,-\,e_\left(f\right)x_=\,e_\left(t\right)x_ solve for x t ( i ) → e θ ( i ) h ( t ) e θ ( i ) ( t ) x t ( i ) = e θ ( i ) h ( t ) x f ^\,\to e_^\left(t\right)e_\left(t\right)\,x_^=\,e_^\left(t\right)x_ set ϵ ( i ) = | | s − e θ ( i ) x ( i ) | | =||s-e_x^||} set θ ( i + 1 ) = θ ( i ) + ∇ ( i ) → ∇ ( i ) = ϵ ( i ) − | | s − e ( θ ( i ) + d θ ( i ) ) x ( i ) | | 2 \,=\,\theta ^\,+\,\nabla ^\,\to \,\,\nabla ^\,=\epsilon ^-||s-e_\,+\,d\theta ^\right)\,}x^||_ set i = i + 1 tamer: advantages and disadvantages advantages: tamer retrospectively corrects for motion, so modifications to the mri exam procedure isn’t necessary. tamer doesn’t alter the acquisition procedure, so it can be easily integrated into current clinical mri scans. tamer significantly reduces computation of the joint optimization model used to estimate motion parameters and image voxels. disadvantages: current tamer implementations have lengthy overall computation times. tamer requires multi-channel data as the motion parameters need additional degrees of freedom which is provided by the multichannel acquisition. the tamer algorithm assumes static coil profiles that don’t change with the motion of the patient. this assumption would be an issue for larger motion. neural network approaches in recent years, neural networks have generated a great deal of interest by outperforming traditional methods on longstanding problems across many fields. machine learning, and by extension neural networks, have been used in many facets of mri — for instance, speeding up image reconstruction, or improving reconstruction quality when working with a lack of data. neural networks have also been used in motion artifact correction thanks to their ability to learn visual information from data, as well as infer underlying, latent representations in data. namer network accelerated motion estimation and reduction (namer) is a retrospective motion correction technique that utilizes convolutional neural networks (cnns), a class of neural networks designed to process and learn from visual information such as images. this is a follow-up from the authors of the tamer paper titled network accelerated motion estimation and reduction (namer): convolutional neural network guided retrospective motion correction using a separable motion model. similar to tamer, the paper aims to correct for motion-related artifacts by way of estimating a desired motion-free image and optimizing parameters for a sense forward model describing the relationship between raw k-space data and image space while factoring in rigid motion. setup a sense forward model is used to induce synthetic motion artifacts in raw k-space data, allowing us access to both data with motion artifacts, as well as the ground-truth image without motion artifacts. this is important to the namer technique, because it utilizes a convolutional neural network (cnn) to frontload image estimation and guide model parameter estimation. convolutional neural networks leverage convolution kernels to analyze visual imagery. here, a 27-layer network is used with multiple convolution layers, batch normalization, and relu activations. it uses a standard adam optimizer. image estimation the cnn attempts to learn the image artifacts from the motion-corrupted input data x . the estimate for these artifacts, denoted as c n n ( x ) , are then subtracted from the motion-corrupted input data x in order to produce a best estimate for the motion-free image: x c n n = x − c n n ( x ) =x-cnn(x)} this serves two purposes: first, it allows the cnn to perform backpropagation and update its model weights by using a mean square error loss function comparing the difference between x c n n and the known ground-truth motion-free image. second, it gives us a good estimate of the motion-free image that gives us a starting point for model parameter optimization. sense model parameter optimization using a cnn effectively allows us to bypass the second stage of tamer by skipping the joint parameter search. this means that we can focus on solely estimating motion parameters θ . because θ is really a vector of multiple, independent parameters, we can parallelize our optimization by estimating each parameter separately. optimizing the optimization procedure before, we used the following to optimize both the image x and parameters θ at once. now, we can optimize solely the θ values: θ ^ = a r g m i n θ ‖ s − e θ x c n n ‖ 2 =argmin_\vert s-e_x_\vert _ on top of this, if a multi-shot acquisition was performed, we can estimate the parameters θ n for each of n shots separately, and go even further by estimating the parameters θ n , l for each line l in each shot n : θ ^ n , l = a r g m i n θ n , l ‖ s n , l − e θ n , l x c n n ‖ 2 _=argmin_\vert s_-e_x_\vert _ this allows us to massively reduce computation time, from around 50 minutes with tamer to just 7 minutes with namer. reconstruction the new model parameters are then used in a standard least squares optimization problem to reconstruct an image that minimizes the distance between the k-space data, and the result of applying the sense forward model e θ ^ under our new parameter estimate θ ^ to our best estimate for the motion-free image: [ x ^ ] = a r g min x ‖ s − e θ ^ x ‖ 2 \vert s-e_x\vert _ this process is repeated until a desired number of time steps, or when the change in reconstructed image is sufficiently low. the namer technique has shown itself to be very effective in correcting for rigid motion artifacts, and converges much faster than other methods including tamer. this illustrates the power of deep learning in improving results across myriad fields. generative adversarial networks other more advanced techniques take advantage of generative adversarial networks (gans) which aim to learn the underlying latent representation of data in order to synthesize new examples that are indistinguishable from real data. here, two neural networks, a generator network and a discriminator network, are modelled as agents competing in a game. the generator network’s goal is to produce synthetic images that are as close as possible to images from the true distribution, while the discriminator network’s goal is to distinguish generated synthetic images from the true data distribution. specific to motion artifact correction in mri, the generator network takes in an image with motion artifacts, and outputs an image without motion artifacts. the discriminator network then differentiates between the synthesized image and ground truth data. various studies have shown that gans perform very well in correcting for motion artifacts. external objects b1 inhomogeneity due to constructive or destructive interference from the permittivity of body tissue can be mitigated using external objects with high dielectric constants and low conductivity. these objects, called radiofrequency/dielectric cushion, can be placed over or near the imaging slice to improve b1 homogeneity. the combination of high dielectric constant and having low conductivity allows the cushion to alter the phase of the rf standing waves and has been shown to reduce signal loss due to b1 inhomogeneity. this correction method was shown to have the greatest effect on sequences that suffer from b1 inhomogeneity artifacts but has no effect on those with b0 inhomogeneity. in one study, the dielectric cushion improved image quality for turbo spin echo‐based t2‐weighted sequences but not on gradient echo‐based t2‐weighted sequences. coil mitigated corrections b1 inhomogeneity has been successfully mitigated by adjusting coil type and configurations. reducing the number of coils one method is as simple as using the same transmit and receive coil to improve homogeneity. this method exploits the tradeoff between b1 dependence and coil sensitivity dependence in flash sequences and allows the user to select an optimized flip angle that will reduce b1 dependence. by using the same coil for transmitting and receiving, the receiver coil sensitivity can offset some of the nonuniformities in the transmitter coil, reducing the overall rf inhomogeneity. for anatomical studies using the flash sequence that can be performed with one transmit and receive coil, this method can be used to reduce b1 inhomogeneity artifacts. however, the method would not be suitable for exams under strict time constraints, since the user first needs to perform flip angle optimization. coil excitation modifying the field distribution within the rf coils will create a more homogenous field. this can be done by changing the way that the rf coil is driven and excited. one method uses a four-port rf excitation that applies different phase shifts at each port. by implementing a four-port drive, the power requirement is decreased by 2, snr is increased by √2, and the overall b1 homogeneity is improved. spiral coil changing the shape of the coils can be used to reduce b1 inhomogeneity artifacts. the use of spiral coil instead of standard coils at higher fields has been shown to eliminate the effects of standing waves in larger samples. this method can be effective when imaging large samples at 4t or higher; however, the proper equipment is required to implement this correction method. unlike post-processing or sequence modulations, changing the coil shape is not feasible in all scanners. parallel excitation with coils another method to correct for b1 inhomogeneity is to employ the infrastructure in place from a parallel system to generate multiple rf pulses of lower flip angles that, together, can result in the same flip angle as that created using a single transmit coil. this method uses the multiple transmit coils from parallel imaging systems to reduce and better mitigate the rf power deposition by relying on shorter rf pulses. one advantage of using parallel excitation with coils is the potential to reduce scan time by combining the multiple short rf pulses and the parallel imaging capabilities to cut scan time. overall, when this method is used with the correct selection of rf pulses and optimized for a low power deposition, the artifacts from b1 inhomogeneity can be greatly reduced. active power modulation actively modulating the rf transmit power for each slice position compensates for b1 inhomogeneity. this method focuses on inhomogeneity along the axial, or z axis, direction since it is the most dominant in terms of poor homogeneity and least sample dependent. prior to inhomogeneity correction, measurement of the b1 profile along the z-axis of the coil is necessary for calibration. once calibrated, the b1 data can be used for active transmit power modulation. for a specific pulse sequence, the values of each slice position are pre-determined and the appropriate rf transmitter power scale values are read from a look-up table. then, while the sequence runs, a real time slice counter varies the attenuation of the rf transmit power. this method is advantageous for reducing artifacts at the source, particularly when accurate flip angle is critical and for increasing signal to noise ratio. even though this technique can only be used to compensate for the b1 variation along the z-axis in axially acquired images, it’s still significant since b1 inhomogeneity is most dominant along this axis. b1 insensitive adiabatic pulses one way to achieve perfect spin inversion despite b1 inhomogeneity is to use adiabatic pulses. this correction method works by removing the source of the problem and applying pulses that will not generate flip angle errors. specific sequences that employ adiabatic pulses for increased flip angle uniformity include a slice selective spin-echo pulse, adiabatic 180 degrees inversion rf pulses, and 180 degrees refocusing pulses. image post-processing post-processing techniques correct for intensity inhomogeneity (iih) of the same tissue over an image domain. this method applies a filter to the data, typically based on a pre-acquired iih map of the b1 field. if a map of the iih in the image domain is known, then the iih