We report the CO ( J = 1 - 0 ) observations of the Whirlpool Galaxy M51 using both the Combined Array for Research in Millimeter Astronomy ( CARMA ) and the Nobeyama 45m telescope ( NRO45 ) . We describe a procedure for the combination of interferometer and single-dish data . In particular , we discuss ( 1 ) the joint imaging and deconvolution of heterogeneous data , ( 2 ) the weighting scheme based on the root-mean-square ( RMS ) noise in the maps , ( 3 ) the sensitivity and uv-coverage requirements , and ( 4 ) the flux recovery of a combined map . We generate visibilities from the single-dish map and calculate the noise of each visibility based on the RMS noise . Our weighting scheme , though it is applied to discrete visibilities in this paper , should be applicable to grids in uv -space , and this scheme may advance in future software development . For a realistic amount of observing time , the sensitivities of the NRO45 and CARMA visibility data sets are best matched by using the single dish baselines only up to 4-6 k \lambda ( about 1/4-1/3 of the dish diameter ) . The synthesized beam size is determined to conserve the flux between synthesized beam and convolution beam . The superior uv -coverage provided by the combination of CARMA long baseline data with 15 antennas and NRO45 short spacing data results in the high image fidelity , which is evidenced by the excellent overlap between even the faint CO emission and dust lanes in an optical Hubble Space Telescope image and PAH emission in an Spitzer 8 \mu m image . The total molecular gas masses of NGC 5194 and 5195 ( d = 8.2 Mpc ) are 4.9 \times 10 ^ { 9 } { M _ { \odot } } and 7.8 \times 10 ^ { 7 } { M _ { \odot } } , respectively , assuming the CO-to-H _ { 2 } conversion factor of X _ { CO } = 1.8 \times 10 ^ { 20 } cm ^ { -2 } [ K \cdot km / s ] ^ { -1 } . The presented images are an indication of the millimeter-wave images that will become standard in the next decade with CARMA and NRO45 , and the Atacama Large Millimeter/Submillimeter Array ( ALMA ) .