How can I repair my component store in Windows 8.1 with a downloaded image using dism.exe?

I'm running Windows 8.1 and I get the following error when I try to repair my system:

    PS C:\WINDOWS\system32> dism /online /cleanup-image /scanhealth /logpath:D:\Downloads\dismlog.txt

Deployment Image Servicing and Management tool
Version: 6.3.9600.17031

Image Version: 6.3.9600.17031

[==========================100.0%==========================]

Error: 14098

The component store has been corrupted.

The DISM log file can be found at D:\Downloads\dismlog.txt

The relevant portion of the log is:

2015-04-03 14:19:55, Info                  DISM   DISM Package Manager: PID=6660 TID=7088  Error in operation: (null) (CBS HRESULT=0x80073712) - CCbsConUIHandler::Error

There's a lot of information in the CBS log but I'm not sure what is relevant. Here is the CBS log.

A repair based on booting the USB image of Windows 8.1 downloaded from MS failed. Windows update failed. It seems like I should be able to fix the component store using the image, but I'm not sure how to go about doing this.

It appears as though the syntax for PowerShell is the following:

Repair-WindowsImage -Online -RestoreHealth -Source G:\sources\install.wim:1

Note that I still get an error back about corruption, but this is what I was looking for. The iso download from Microsoft didn't have a wim file, but I did use a free program to convert install.esd to install.wim.