This processing is one of the bottlenecks in digital camera speed, so manufacturers put much effort into making, and marketing, the fastest processors for this step that they can.
Sony designs the circuitry of the processor in-house, and outsources the manufacturing to semiconductor foundries such as MegaChips and (mostly) GlobalFoundries, as they currently do not own any fabrication plant capable of producing a system on a chip (SoC).
[1] Sony also sources DRAM chips from various manufacturers namely Samsung, SK Hynix and Micron Technology.
The first chip is an SoC that manages overall functionality of the camera such as SD card storage management, wired connection such as USB and HDMI, and wireless protocols such as Wi-Fi and NFC that are increasingly common on modern Sony α cameras.
The latter is based on a quad-core ARM Cortex-A5 architecture, and is utilized to run Android apps on top of the Linux kernel.