Linear shift-invariant spatial filtering is applied to inversion of radiometric measurements of the earth in both polarizations at frequencies of 6.6, 10.7, 18, 21, and 37 GHz. The state of the ocean-atmosphere system, for the purpose of radiative transfer calculations at these frequencies, is described by a seven-parameter model. The parameters are sea surface temperature, near-surface wind speed, integrated water vapor mass, scale height of water vapor in an exponential distribution, integrated liquid water mass, height of the liquid water, and characteristic drop radius in a Best drop size distribution. Nonlinear dependence of brightness temperature on these parameters is approximated by second-order terms in the parameters. Residual nonlinearity of the system appears theoretically as cross talk from the second-order terms to the first-order terms. Given the linear filter structure, the filter coefficients are obtained by minimizing the expected square error, which includes both first- and second-order components of cross talk, noise, and fine-structure error. The last is the result of incomplete restoration of the geophysical parameter fields. Thus the spatial filter deconvolves and inverts the data simultaneously. The two heights are found not to be recoverable from the measurements, however.