Well, judging from the article HSBC (Orchard Bank) could be a good option for you as it says: “Applicants who provide a security deposit get approved, unless a background check with the credit bureaus turns up a discrepancy related to the identity of the applicant.” It doesn’t say anything about income.
Plus, ambersun just mentioned on another thread that they have a pre-approval form to see if you qualify (soft inquiry).