Stable recovery of planar regions with algebraic boundaries in Bernstein form

Abstract We present a new method for the stable reconstruction of class binary images from small number measurements. The we consider are characteristic functions algebraic domains, that is, domains defined as zero loci bivariate polynomials, and assume to know only finite set uniform samples each image. solution such problem can be up in terms linear equations associated image moments. However, sensitivity moments noise makes numerical highly unstable. To derive robust recovery algorithm, represent polynomials corresponding Bernstein apply polynomial-generating, refinable sampling kernels. This approach is noise, computationally fast simple implement. illustrate performance our algorithm noisy through extensive experiments. Our code released open source freely available.