Learned sparse retrieval (LSR) is a family of neural methods that encode queries and documents into sparse lexical vectors that can be indexed and retrieved efficiently with an inverted index. We explore the application of LSR to the multi-modal domain, with a focus on text-image retrieval. While LSR has seen success in text retrieval, its application in multimodal retrieval remains underexplored. Current approaches like LexLIP and STAIR require complex multi-step training on massive datasets. Our proposed approach efficiently transforms dense vectors from a frozen dense model into sparse lexical vectors. We address issues of high dimension co-activation and semantic deviation through a new training algorithm, using Bernoulli random variables to control query expansion. Experiments with two dense models (BLIP, ALBEF) and two datasets (MSCOCO, Flickr30k) show that our proposed algorithm effectively reduces co-activation and semantic deviation. Our best-performing sparsified model outperforms state-of-the-art text-image LSR models with a shorter training time and lower GPU memory requirements. Our approach offers an effective solution for training LSR retrieval models in multimodal settings. Our code and model checkpoints are available at github.com/thongnt99/lsr-multimodal