  The goal in signal compression is to reduce the size of the input signal
without a significant loss in the quality of the recovered signal. One way to
achieve this goal is to apply the principles of compressive sensing, but this
has not been particularly successful for real-world signals that are
insufficiently sparse, such as speech. We present three new algorithms based on
solutions for the maximum feasible subsystem problem (MAX FS) that improve on
the state of the art in recovery of compressed speech signals: more highly
compressed signals can be successfully recovered with greater quality. The new
recovery algorithms deliver sparser solutions when compared with those obtained
using traditional compressive sensing recovery algorithms. When tested by
recovering compressively sensed speech signals in the TIMIT speech database,
the recovered speech has better perceptual quality than speech recovered using
traditional compressive sensing recovery algorithms.
