The invention relates to a joint constraint 
random noise suppression method based on 
sparse regularization, and belongs to the technical field of geophysical exploration. The method specifically comprises the following steps: S1, inputting an original seismic 
record, and constructing an objective function of 
curvelet transform-second-order generalized total variation joint constraint denoising according to sparse features of 
noisy data in a 
curvelet domain and an 
image gradient domain; S2, converting the L1-L2 norm regularization model containing the 
curvelet transform constraint term into a standard basis pursuit 
noise reduction problem, and inverting a curvelet coefficient with the minimum L1 norm to obtain a seismic 
record after preliminary denoising; and S3, taking the preliminarily denoised seismic 
record as an input image, solving a denoising problem of the second-order generalized total variation constraint to realize 
random noise suppression of the joint constraint, and finallyoutputting seismic data with an enhanced 
signal-to-
noise ratio. According to the method, the denoising effect on 
random noise in the seismic data is improved, and 
weak signal energy can be effectively protected, so that high-quality 
processing of subsequent seismic data and the reliability of a seismic geological interpretation result are guaranteed.