  Intensity mapping observations measure galaxy clustering fluctuations from
spectral-spatial maps, requiring stable noise properties on large angular
scales. We have developed specialized readouts and analysis methods for
achieving large-scale noise stability with Teledyne 2048$\times$2048 H2RG
infrared detector arrays. We designed and fabricated a room-temperature
low-noise ASIC Video8 amplifier to sample each of the 32 detector outputs
continuously in sample-up-the-ramp mode with interleaved measurements of a
stable reference voltage that remove current offsets and $1/f$ noise from the
amplifier. The amplifier addresses rows in an order different from their
physical arrangement on the array, modulating temporal $1/f$ noise in the H2RG
to high spatial frequencies. Finally, we remove constant signal offsets in each
of the 32 channels using reference pixels. These methods will be employed in
the upcoming SPHEREx orbital mission that will carry out intensity mapping
observations in near-infrared spectral maps in deep fields located near the
ecliptic poles. We also developed a noise model for the H2RG and Video8 to
optimize the choice of parameters. Our analysis indicates that these methods
hold residual $1/f$ noise near the level of SPHEREx photon noise on angular
scales smaller than $\sim30$ arcminutes.
