1. A method, comprising: applying, using processing circuitry including a processor and memory, an approximate message passing (AMP) conversion framework to a plurality of substantially linear measurements of a multi-dimensional signal for conversion into a plurality of scalar measurements, where the multi-dimensional signal comprises a two-dimensional image or a three-dimensional hyper spectral image or volume; applying, using the processing circuitry, a non-scalar denoiser algorithm to the plurality of scalar measurements to generate a plurality of denoised scalar measurements; and applying, using the processing circuitry, a conversion term to the plurality of denoised scalar measurements for converting the plurality of denoised scalar measurements to a plurality of denoised substantially linear measurements.