[MUSIC] Okay, we will talk about the concept of resolution in this video. So in MRI, the k-space covers only a finite region in the frequency domain. So because of that, MRI is a kind of lowpath filter, because it covers only certain middle ranges. So it cannot cover all the way out off the way infinitely the area of the k-space. So MRI can be considered as a lowpath filter. The special resolution along the frequency encoding and phase encoding encryptions can be defined as field of view divide by number of sampled points, okay? Delta x through a special resolution can be formulated as field of view divided by number of points which is obvious. So based on the previous equations, field of view X can be represented in a common GxTs, which is one step sides on the frequent K base, on the extras of Kx. Comma Tx Ts, and that is, multiplied by number of sampled points, okay? Again, this portion determines one sampling point, data u or data kx, and that is multiplied by no both sample points. That means this mx delta kx, or this denominator, represent whole range of the case base, okay? So because on the case base, one sample size is delta K, X, then multiply by number of samples. Okay, that represent whole case base range along the x direction. And y direction also the same thing, okay? That represent whole range of the case base along y direction. So this spatial resolution, so one pixel size on the image domain corresponds to the whole range of the k-space, okay? So the spatial resolution of an MR image is inverse of the the maximum k-space ranges, so Nx, delta k x, Ny delta k y. So spatial resolution and field of view. They have a certain kind of inverse relationship in the viewpoint of k space. So field of view corresponds to one step size on the k space, and resolution corresponds to the maximum k space range. They have inverse relationship in the viewpoint of k space, okay? So in this figure, it shows the case with the reader. One case, or reader. And then, this this case shows compared to the previous, this example, where it has twice longer time. For the sampling, which means k space range is going to be twice bigger. Then what happen to the image if we change the sampling scheme compared to this case? If this case samples images like that and this one samples much bigger range for the k space. But number of points are fixed, but what will happen to the template image? And if samples with smaller field of view, okay? Smaller field of view, but number of templates are the same, so that increase space, that increases spacial resolution, okay? Because field of view gets reduced, the reason is field of view of the images corresponds to the one sample size on the k-space. Because of that, this field of view gets small because this one sample size gets bigger by changing sampling scheme like that. So this step size gets bigger which means this imaging field of view gets smaller because they have inverse relationship, okay? But number of samples aren't a thing, because of that sampling, the resolution has increased compared to the previous case, okay? The same thing is also true if we maintain the time for sampling or increase gradient strength twice. Compared to the previous one, compared to this regional case. In the previous slides, time was twice longer, and that also increase the area on the case base. The same thing is true, if we increase gradient strength, but the time is maintain. But they will give the same region. So case based, maximum range match increased. So in this case, again, the sample, case-based sampling period, this delta Kx becomes bigger, that means field of view gets small. Okay, so you can decrease field of view increasing the spacial resolution. Okay, because the number of samples are the same, but the field [INAUDIBLE] are reduced. So the spacial resolution gets increased, okay? The last case is the area. So time is actually reduced by half compared to the original case. But the strength got an increase of twice then total area remained the same. And then, the k-space area is going to remain the same. Then field of view and spatial resolution will not change. So there will be no change in the resolution and no change in the field of view.
