Photonic sources readily provide several THz of analog bandwidth for information processing. Taking advantage of this fact, problems such as ultrawideband radio (RF) spectrum sensing, high performance radar, and analog-to-digital conversion can achieve significant performance gains with photonic techniques. Likewise, photonic imaging systems such as time-stretch microscopy have produced a breakthrough in continuous high speed imaging, enabling faster shutter speeds, higher frame rates, and greater gain-bandwidth product than is possible with continuous read-out CCDs and CMOS sensor arrays. However, imaging at this rate with traditional Nyquist sampling inevitably yields sustained data output on the order of 100 Gb/s or more, creating a significant challenge for storage and transmission. Real images and video are highly compressible, so this deluge of data is also highly inefficient.This thesis will address several techniques based on chirp-processing of ultrafast laser pulses that demonstrate real-time efficient compression of both electronic and optical signals, overcoming electronic bottlenecks via optical processing in the analog domain. Several systems will also be presented that permit greater information extraction from high throughput microscopy experiments by measuring quantitative phase images on a time-stretch microscope.